Statistics Questions and Answers March 07, 2024

Save AllSW Consider independent Exponential variables distribution of YXXX, is Oa. Gamma (3, 0) Ob. Exponential (03) Oc. Gamma (3, 0) Od. Exponential (30) 1 XXX, all with parameter 0, then the 23

1. An urn contains four balls numbered 5, 6, 7, and 8. If two balls are drawn from the urn at random (first take one, replace it and then take one replacement) and Z is the sum of the numbers on the two balls drawn, find (a) the probability distribution of Z (b)the distribution function of Z. (c) Find E(Z)

How can I find the exact p-value for each coefficient (p>t )column if the number of observations = 52, df numerator is 3, df denominator is 48, t static is there in the third column. I need to know the exact number for p>t each rows.

eq 1 The following is STATA output from a two variable OLS regression on gas consumption that we demonstrated in class Source SS df MS Model 2.7723 Residual 0.136253108 Total 2.90855 3. N 00283 0.924108071 48 D 50 Std. Err. t Ka NK Number Number of obs F(,) Prob F Rsquared Adj Rsquared Root MSE 1 .9531 053 27 2.0423 4 XXN Log gas Post Coef. dung

A battery company has found that the defective rate of its batteries is 0.05. Each day, 7 batteries are randomly tested. Find the probability that exactly 1 is found to be defective.

You roll a 6sided die. What is the probability that you will roll either a 6 or a 5 P(6 or 5) You flip a 2sided coin. What is the probability that you will get either heads or tails P(heads or tails)

BINGO The game of bingo involves drawing labeled balls from a bin at random (without replacement). There are 75 balls, 15 for each of the letters B, I, N, G, and O. Round your answers to three decimal places. What is the probability of drawing two G balls in the first two selections Answer What is the probability of drawing a N on the second

In Canada, about 21.56% of women over 40 will develop breast cancer in any given year. A common screening test for cancer is the mammogram, but it is not perfect. In about 36.21% of patients with breast cancer, the test gives a false negative: it indicates a woman does not have breast cancer when she does have breast cancer. Similarly, the test

The Stanford Five-City Project is a comprehensive community health education study of five moderately sized Northern California towns. Multiple-risk factor intervention strategies were randomly applied to two of the communities. The other three cities served as controls. Outline the design of this study in schematic form.

Suppose you use a random number generator on the internet to choose random numbers between 1 and 9. The random number generator has an equal probability of choosing any of those numbers. a) What probability distribution does this represent and how do you know b) What is the expected value of this distribution Show work. c) Does the expected value

Let Yi (Y1,..., YiT) and Y be an i.i.d. sample. Further suppose that Yit A B Vit with E Vit 0 and where we treat A, and Bt as parameters to be estimated. Let D be as in (4.36) and consider estimating (A,..., An) and (B,..., BT) by T T (a A) mx arg min aER, bERT n YiDa1t tbt i1 t1 f1 (a) Derive a closed form expression for , by using Theorem

Suppose that the density (pdf) function for a random variable X is given by f(x) for 0 x2 and f(x) 0 otherwise. What is the probability P(0.5 x 1) Round your answer to four decimal places. 2

Two cities, New York and Chicago are experiencing a tremendous upsurge in criminal activity ever since the defund the police campaign started. There is competition between the two cities to decrease the violence. The local paper recently reported that the mean number of criminal activities in New York is 52 per day with a standard deviation of 6

You are playing with a standard 52-card deck. Every time you draw a card from the deck, you put the card back and shuffle the deck again before choosing another card. What is the probability of rolling a number between (but not including) 6 and 10?

A committee has nine members. There are three members currently serving as board president and treasurer. Each member has an equal chance of serving in either position. Three members are randomly selected and assigned to be the new president and treasurer. What is the probability of randomly selecting the three members currently holding the

The mean number of words per minute (WPM) read by sixth graders is 81 with a standard deviation of 17 WPM. If 130 sixth graders are randomly selected, what is the probability that the sample mean differs from the population mean by more than 2.11 words per minute?

A research question that could be asked using the available data: Is there any advantage to never having smoked when it comes to the severity of CoVID-19?Essentially, we would like to know if the high severity rate of CoVID-19 is lower for never smokers than for current/former smokers. Determine a method that would be appropriate to answer this

A survey on youth and smoking contacted 300 smokers and 300 non-smokers by telephone, all aged 14 to 22 years. What study design is this?

Superabsorbent polymer (SAP) is a hydrogel capable of absorbing liquids through hydrogen bonding. A homecare products company is looking to increase the absorbency of its leading diaper brand by incorporating a newly improved low-density cross-linked SAP into the product. To test whether the improved SAP statistically significantly improves the

The New England Journal of Medicine posts its peer-reviewed articles and editorials on its website. An opt-in poll was featured next to an editorial about the regulation of sugar-sweetened beverages. The poll asked, Do you support government regulation of sugar-sweetened beverages? Readers just needed to click on a response (yes or no) to become

A manufacturer of pharmaceutical products analyzes each batch of a product to verify the concentration of the active ingredient. The chemical analysis is not perfectly precise. In fact, repeated measurements follow a Normal distribution with mean equal to the true concentration and with standard deviation grams per liter(g/l). Three random samples

A 2012 Gallup survey of a random sample of 1014 American adults indicates that American families spend, on average, $151 per week on food. The report further states that, with 95% confidence, this estimate has a margin of error of $7. a) This confidence interval is expressed in the following form: estimate margin of error. What is the range of

A cubit is a distance measurement from the ancient Near East that equals approximately 1.5 feet. If a ziggurat (a cool pyramid... google it for more info) covers an area of 2,069 cubits2, what is its area in square meters?

Purchase land worth $54,000 to create a community garden.To do this, you take out a 10-year loan, with an APR of 5.22%, compounded monthly, and requiring monthly payments of $505.(Assume the value of the land is still $54,000. Round each answer to the nearest dollar.) (to) Assuming you made a down payment, what was your original loan amount (in

Two parabolas have the same x-intercept s of 0 and 10 . One has a maximum of 2 while the other has a minimum of -4 . Sketch the parabolas.

Suppose two marbles are drawn without replacement from a box with 1 blue, 3 white, 2 green, and 2 red. Find the probability that the second marble is red, given that the first marble is red.

Consider a sequence of coin tosses with probability p of coming up heads (H).Use a martingale argument to calculate the expected value of the rolls until the next sequence appears.where H = heads and T = tails 1) H,H,T,T,H,H,T 2) H,T,H,T,H,T

Events occur according to a Poisson process of rate .Every time an event occurs, we will get a prize and we must decide whether to stop or not, our goal being to stop at the last event that occurs before a specific time T with T > 1/.That is, if an event occurs at time t, 0 t T, and we decide to stop, then we win if there are no additional

Box A Purple Pens 10 Box A Red Pens 23 Box B - purple pens 16 Box B - red pens 8 5. Name an event with either box A or box B where the probability would be 3.

A chemical warehouse stores a collection of 40 gas cylinders consisting of 22 flammable gas cylinders and 18 inert gas cylinders. A group of 17 cylinders is randomly selected from the 40. Find the probability that the selected group has 9 flammable gas cylinders and 8 inert gas cylinders.

4. Use the below contingency table to find the following probabilities. Republican Democrat Libertarian Christian 40 7 3 Muslim 8 30 12 Jews 25 15 10 (a) What is the probability that a randomly selected person is either Republican or Muslim Bule (b) What is the probability that a randomly selected person is either Democrat or NOT a muslim (c) What

i) Let M and N are two events such that, P(M) 0.8, P(N) 0.135, P(MN)0.2. Calculate the probability, P(MC NC). ii) A random experiment indicates that P (E1) 0.12 and P (E2) 0.14. Given that the experiment consists of 4 simple events. Find P (E3) and P (E4), if they are equally likely.

For the following problems, name the type of probability distribution that can be used for each case. 1. Of all customers purchasing automatic garage door openers, 75% purchase a chain-driven model. Let X = the number among the next 15 purchasers who select the chain-driven model. 2. Draw marbles from a bag containing 5 red marbles, 6 blue marbles

The details of clock sales at a supermarket for the past 6 weeks are shown in the table below. The time series appears to be relatively stable, without trend, seasonal, or cyclical effects. The simple moving average value of k is set at 2. Week Units Sold 2period Moving Average Error Absolute Error 1 15 NA 2 18 NA 3 13 16.5 3.50 3.50 4 16 15.5

The following data contains days when road rage occurred according to a study, The goal of the study is to determine when road rage occurs most often. F1F,W,M,M,M,M,Sa,Su,F,F,M,Th,Su,F,F,Su,F,Tu,F,F,Tu,W,Th,F,Th,Sa,F,W,M,Tu,Th,Tu,F,F,W,F,Tu,Su,M,F,Th,Th,Th,Tu,F,Sa Find the mode of the above data.

hours and a standard deviation of 0.8 hour. A student is randomly selected. he times per week a student uses a lab computer are normally distributed, with a mean of 5.4 (a) Find the probability that the student uses a lab computer less than 8 hours per week. (b) Find the probability that the student uses a lab computer between 3 and 6 hours per

A quantitative data set has mean 20 and standard deviation 3. Apply Chebyshevs rule to complete parts (a) and (b) below. a. At least 96 of the observations lie between which two values At least 96 of the observations lie between 5 and 35. (Round to the nearest whole number as needed.) b. What percent of the observations lie between 11 and 29 At

Find the probability that the mean of a sample of 25 people is between 11 and 12 P(11 12)

. Suppose you roll a fair 6sided dice for a random trial. (Laplace). Let B represent the event that the sum of two rolls is Less than or equal to 2, and A represents the event that the sum of two rolls gives you a value greater than or equal to 11. What is the conditional probability of B given A Are they mutually exclusive Are they independent

This year a sample of 100 babies showed that 23 weighed over 7 pounds 5 ounces. -> Construct a 95% confidence interval for the true proportion of babies born in the hospital weighted more than 7 pounds 5 ounces. Round the final answers to three decimal points

The following are the ratings of males by females in an experiment involving speed dating. Use the given data to construct a boxplot and identify the 5number summary 1.0 2.0 25 2.5 3.0 3.0 4.0 4.0 4.0 4.0 4.0 4.5 5.5 5.5 5.5 5.5 6.5 6.5 7.0 8.0 The 5number summary is and (Use ascending order. Type integers or decimals. Do not round.)

1. A company (the producer) supplies microprocessors to a manufacturer(the consumer) of electronic equipment. The microprocessors are supplied in batches of 50. The consumer regards a batch as acceptable provided that there are not more than 5 defective microprocessors in the batch. Rather than test all of the microprocessors in the batch, 10 are

Seventeen percent of U.S. residents are in their thirties. Consider a group of eight U.S. residents selected at random. Find the probability that at least five of the people in the group are in their thirties The probability that at least five of the people in the group are in their thirties is (Round to four decimal places as needed.)

The probability that a live birth requires a cesarean delivery in a certain American state is 0.313. If 5 live births occur independently in this state, compute the probability that at least one of the births requires a cesarean delivery.

2. Two urns contain white and black balls Urn 1 contains 10 black balls and 5 white balls, Urn 2 contains 8 black balls and 2 white balls. Two balls are drawn randomly from urn 1, and these two balls are then placed in urn 2. Then, two balls are drawn randomly from urn 2. a. What is the probability that both balls drawn from urn 2 are white b.

The temperature (in oC) in a certain city follows a Normal distribution with mean 20. Which would be the standard deviation if we know that the probability that the temperature is between 16 and 24 is around 0.5?

In a population with an average, = 3, 000 and a variance, 2 = 36,000. Answer the following: (a) If you draw a random sample of 1,000 observations, what is the probability that the sample mean will be greater than 3,011.76 or less than 2,988.24? (b) If you draw a random sample of 4,000 observations, what is the probability that the sample mean

Mamu marketing manager belief that in a day 300 customers come into the restaurant. He has collected the data for the last three months. i) Hypothesis (H0 and H1) ii) One-tailed (upper tailed or lower tailed) or two tailed. iii) Illustrate the distribution curve, the side of the tail and the rejection and non-rejection region. the question only

It is reported that female students spend more than 30 minutes daily doing make-up. A researcher believes the average time spend on make-up is lower. i) Hypothesis (H0 and H1) ii) One-tailed (upper tailed or lower tailed) or two tailed. iii) Illustrate the distribution curve, the side of the tail and the rejection and non-rejection region.

On the Navajo Reservation, a random sample of 214 permanent dwellings in the Fort Defiance region showed that 52 were traditional Navajo hogans. In the Indian Wells region, a random sample of 139 permanent dwellings showed that 23 were traditional hogans. Let p1 be the population proportion of all traditional hogans in the Fort Defiance region,

report issued by Malaysia Insurance Institute (MIM) reported that the average premium for health insurance per customer aged between 40-50 within RM250 per month. An individual claims that the average premium per month is less than RM250 Determine the followings for each of the given statements: i) Hypothesis (H0 and H1) ii) One-tailed (upper

Question C 1. 8 Let A be a sequence of independent events such that P(A) n1 1. The probability P(An i.o.) is n log n 1. 1 1 2. 2log 2 3. O

To see if event A and event B are independent of each other, test if P(A|B) = P(A) or if P(B|A) = P(B). If the two sides of the equation(s) are equal, then the two events are independent. That is, the occurrence of event B does not influence the probability of the occurrence of event A, or the occurrence of event A does not influence the

Two dice were rolled forty times and then the sum of the two dice were calculated after each roll. Complete the following calculations. Sums: 9, 8, 9, 8, 7, 4, 3, 7, 11, 9, 7, 6, 7, 10, 12, 6, 6, 4, 7, 5, 7, 7, 10, 7, 8, 8, 6, 8, 7, 11, 7, 6, 9, 9, 8,3, 10, 7, 8, 4 2. Find the null and alternative hypotheses. 3. Indicate the distribution that the

Many problems depend on the evolution of states over time. Consider the state space diagram below (inspired by the Hidden Markov Model) and answer the following questions. This week we are just getting comfortable with conditional probabilities. In this example, the only unknown parameter is . (a) Write P (Xt = 1|Yt = 5, Xt+1 = 1) in terms of .

X Bernoulli(0) Xt X1 XX Bernoulli(0.9 0.8.X) Y1 YX Binomial(n 10, p 0.70.1X) Y 2 YX1 Binomial(n 10, p 0.1 0.8X11)

Monitors manufactured by TSI Electronics have life spans that have a normal distribution with a variance of 1,960,000 and a mean life span of 20,000 hours. If a monitor is selected at random, find the probability that the life span of the monitor will be less than 22,379 hours. Round your answer to four decimal places.

The daily demand for a spare engine part is a random variable with a distribution based on past experience, given by The part is expected to be obsolete after 400 days. Assume that demands from one day to the next are independent. The parts cost $1500 each when acquired in advance of the 400 day period and $5000 each when purchased on an emergency

Number of Demands per day Probability 0 1 23 .21 .38 .19 .14 4 .08

Question 1 1 pts You decide to use 2digit hexadecimal strings for your ciphertext. That is, each character will look like XX, where each X is from the set 0,1,..., 9, A, B,..., E, F. You want to tie each plaintext character (az) to a set of ciphertext elements so that the relative frequency of each ciphertext element is roughly equal. How many

Humber Bakery needs to decide how many units of its new Rexdough bread (nicknamed Rex) to bake at the start of each day.Because the bakery prides itself on being the maker of the freshest premium bread in town, units that don't sell at the end of the day are discarded and considered a loss.Each Rexdough loaf costs $1.18 to produce and sells for

The tents have capacity for 2, 3, 5, 6 or 12 people. How many tent combinations are possible to sleep 26 if all tents are fully occupied and exactly one 12-person tent is used?

A bag of fruits contains 5 apples, 3 bananas, and 2 oranges. In each draw, a fruit is drawn from the bag and not replaced. In three draws, find the probability of obtaining an apple, a banana, and an orange in that order.

Use the spinner to find each theoretical probability a). P (a number no more than 5) b). P (an even number) c). P (a number less than 3)

8 7 1 2 6 5 3

A foundry produces automobile brake pads. A specific lot of 70 of these pads includes 10 with burrs that were overlooked in the manufacturing process. If a part is randomly selected from the lot to be installed in an automobile, what is the probability that it will have burrs?

3. Consider the random variable X The number of even numbers showing when a pair of standard sixsided dice are rolled. a. Create the probability distribution for X. b. Find the mean of X. c. Find the standard deviation of X. d. Suppose that Y the amount won when playing the following game You pay 5 dollars to play, but win 2 for each even number

Two cards are drawn with replacement from a standard deck of 52 cards. a.what is the probability that the second card is a diamond if the first card drawn was a queen of clubs? b. are these events independent or dependent? Explain

A green and red die are rolled. Find the probability of the following events: a. The sum of the numbers on the dice is less than five. b. One die gives a four and the other die a number less than three. c. The sum of the numbers on the dice is three or 11. d. The sum of the numbers on the dice is eight or both die have the same number. e. The sum

consider a decision maker who, when confronted with a choice between a lottery that would give her 4 for sure and a lottery that would give her 10 with probability, 4 with probability, and 0 with probability, would strictly prefer the first lottery and, when confronted with a choice between a lottery that would give her 4 with probability and 0

Spacely Sprockets manufactures 31% of their sprockets on Neptune, and the remainder on Pluto. Of the sprockets made on Neptune, 2.3% are defective. Of the sprockets made on Pluto, 1.5% are defective. What fraction of all defective sprockets were manufactured on Neptune? [You may want to use a tree diagram.]

Assume that every time you buy an item of the Hong Kong Disney series, you receive one of the four types of cards, each with a cartoon character Mickey, Minnie, Donald and Daisy with an equal probability. Over a period of time, you buy 6 items of the series. What is the probability that you will get all four cards

Consider a single server queue system (e.g., a food truck). It follows a FIFO (FirstIn and FirstOut) rule and let consider the time frame from t 0 to t 10 at this case. Customers arrivals and service times are Customer ID Arrival time (min) Service time (min) 1 1 2 3 3 4 4 5 3 4 1 3 (A) Draw a plot for representing number of customers Q(t) in

A large company is planning to replace its application for employees time reporting with a new application. The seller of the new application indicated that 9 0 % of its customers are happy with their application. If the company selects a random sample of 1 5 0 employees, what is the probability that at least 9 0 % of them say they are happy with

Chapter 8 Interval Estimation Managerial Report 1. Use appropriate descriptive statistics to summarize each of the three variables for the 40 Gulf View condominiums. 2. Use appropriate descriptive statistics to summarize each of the three variables for the 18 No Gulf View condominiums. 3. Compare your summary results. Discuss any specific

1. A fair coin is flipped five times. What is the longterm probability that for every five times it is flipped there will be exactly 3 heads Show all needed work. Round your answers to 3 decimal places. 2. A coin is flipped 4 times. Fill in the probability distribution for the probabilities of all possible outcomes for the coin to land on heads.

1. From a recent census in a particular residential area it was found that 95 of residents had English as their main language and 30 of the population were under 18 years old. The local library wants to explore this issue and decides to create a sample of 200 people. (a) In a stratified sample, how many of the 200 people should be 18 years old or

For this game, complete the tree diagram below by calculating numeric values for the probabilities along the labelled branches (large bold text), and the overall probability of winning P4 All different WIN . All different P3 All different P2 P1 All different 2 cards the same card 3 2 cards the same Lose on card 4 Lose on 2 cards the same Lose

A company is considering three different projects (A, B, C) in an attempt to diversify. The effectiveness of each project (in terms of revenue) are dependent upon the level of the economy. There five possible levels (15) based on economic projections. The assumed probability of each level occurring are listed below. Probability 0.2 Outcome 1 2 0.1

A pet store has 5 birds, 8 dogs, 3 cats and 4 lizards. A person walks into the store and wants to purchase 3 pets. Assuming equally likely outcomes, what is the probability that all 3 pets are of the same species

Your quadcopter has a terrible altitude sensor. To see how bad it really is you take many measurements with the quadcopter at 1 meter altitude. Your altitude sensor gives a mean of 1.00 meters with a standard deviation of 13cm. The measurements are normally (Gaussian) distributed. What is the probability that your altimeter gives an error of less

Suppose that you flip 50 honest coins. (a) How many microstates are there Give your answer as a factor of the order of unity times an integral power of 10. (b) How many microstates are there corresponding to the most probable macrostate (c) What is the true probability of achieving the most probable macrostate

Provide the following answer using the following compound below. a. Assign the hybridization for each atom, except hydrogen. b. Determine the number of atomic orbitals and Molecular orbitals (AO, MO). c. Draw the atomic orbitals for each atom and their MO d. Draw the energy diagram. e. Assign the HOMO and LUMO in the energy diagram. H HCCECH 10

According to Ohms Law, the voltage V, current I, and resistance R in a circuit are related by the equation V IR, where the units are volts, amperes, and ohms. Assume that the voltage is constant with V 17 V. Calculate the average rate of change of I with respect to R for the interval from R 9 to R 9.1. (Use decimal notation. Give your answer

5. Recent data collected by Pioneer show 38.2 of plots planted with the X19 seed formula exceed expected yields, whereas 12.8 of plots planted with other formulations perform similarly. During last years crop cycle, 27.3 of plots used the X19 seed formula. Given that a randomly selected plot exceeded expected yields, what is the probability it was

Next week, the number of projects that will require you to work overtime has a Poisson distribution with mean 1. For each project, the distribution of the number of overtime hours in the week is the following: x f(x) 5 0.2 10 0.3 20 0.5 The number of projects and number of overtime hours are independent. You will get paid for overtime hours in

1. The following table summarizes the opinion about afterlife for different races and gen ders from a General Social Survey. The response is belief in life after death yes, 2 undecided, 3 no), and the two explanatory variables are gender (1 females, 0 males) and race (1 whites, 0 blacks). Fit a baselinecategory logit model b log(Tk3)ak x1

Why is it not possible to have 100% confidence? Explain. (Choose Best Answer Below) a.)A 100% confidence interval is not possible unless either the entire population is sampled or an absurdly wide interval of estimates is provided. B.) A 100% confidence interval is not possible only if an absurdly wide interval of estimates is provided. C.) A 100%

1. A single sampling plan is used. 15 samples are taken for the test. It is known that 8 of the samples from the production lime are found to be defective. Calculate the probability of acceptance and the producers risk assuming the distribution is based on binomial distribution. i) The acceptance number is 1. AQL 0.08, n15, c 1 ii) the

My mother is a very active woman. On any given day there is a 75% chance she will jog, a 20% chance that she will play golf and a 30% chance that she will pickle ball. She never plays pickle ball on the same day she plays golf. There is a 5% chance that she will jog and play pickle ball and a 15% chance that she will jog and play golf. a. What is

The Ski Trip Probability The ski club you belong to is off on another trip. This time you invite 2 of your friends to join. You are excited and very hopeful the three of you will be assigned to the same 4-person chair lift. There are only 13 other people on the trip, besides you and your two friends. So, you are hoping for good odds! 1. Calculate

1. Roll a regular sixsided die ten times and record the rolls. (If you do not have a die, google virtual dice roller.) 2. Calculate the mean of the rolls. 3. Calculate the median of the rolls. 4. Calculate the mode of the rolls. 5. Calculate the range of the rolls. 6. Calculate the standard deviation of the rolls. 7. List the five number summary

A customer at Cavallaros Fruit Stand picks a sample of 4 oranges at random from a crate containing 45 oranges, of which 6 are rotten. What is the probability that the sample contains 2 or more rotten oranges (Round your answer to 3 decimal places and be sure the explain your answer.),4. (6 points) An automobile manufacturer obtains the

The personnel department of Franklin National Life Insurance compiled the accompanying data regarding the income and education of its employees. Income $60,000 or Below Income Above $60,000 Noncollege Graduate 1920 890 College Graduate 410 780 Let A be the event that a randomly chosen employee has a college degree, and let B be the event that the

Verify that the following function is a probability mass function, and determine the requested probabilities Give exact answers in form of fraction. f(x) (78) (18), x 0,1,2,... (a) P(X 2) (c) P(X 2) (b) P(X 2) (d) P (X 1)

The owner of a restaurant is examining its use of eggs. Based upon past experience, the owner believes that daily egg use is distributed normally with a mean of 56 and a standard deviation of 11. What is the probability that the restaurant will use between 69 and 76 (inclusive) eggs in a given day

A researcher is interested in whether blind Braille readers could be taught to read faster using the same techniques as sighted readers. He has blind adults complete a reading speed test before and after a sixweek speedreading course. In the beginning of the study, a randomly selected group of 121 blind Braille readers scored an average of 261

A test requires that you answer first Part A and then either Part B or Part C. Part A consists of 7 truefalse questions, Part B consists of 9 multiple choice questions with one correct answer out of 5. and Part C requires you to match 8 questions with 8 different answers. (Each question matches exactly one correct answer.) How many different

Consider the objective function to maximize profit Max 2A B S.T. Constraint 1 A B 1.5 nonnegativity A,B 0 Assume the optimal solution is A3.5 and B0. Which of the following is FALSE If we set A and B to be integers, the new total profit will increase If A and B are continuous, the total profit is 7 If we set A and B to be integers, the optimal

7. Of 300 students in a large accounting course, 15 are taking six other courses, 35 are taking five other courses, 175 are taking four other courses, 50 are taking three other courses, and the rest are taking two other courses. How many courses do you expect a randomlyselected student from the accounting course to be taking

Dan Mullen is employed by a mail-order distributor and reconditions used desktop computers, broadband routers, and laser printers. Dan is paid $12 per hour, plus an extra $6 per hour for work in excess of 40 hours per week. The distributor just announced plans to outsource all reconditioning work. Because the distributor is pleased with the

Suppose X and Y are binary random variables, each taking the values 0 and 1. If we know that the event X x is independent of the event Y y, i.e x 1 y, does it mean that XLY Give mathematical justifications for your answer. What about the case when X and Y are nonbinary random variables that take more than two values each 6 Marks

3. Suppose that you are interested in choosing a set of investments 1,,7 using 0 1 variables. Model the following constraints using only linear equations (obs operators such as or or if can not be used) (a) You cannot invest in all of them. (b) You must choose at least one of them. (c) Investment 1 cannot be chosen if investment 3 is chosen. (d)

In a school of 500 students, 60% of the students play a musical instrument. Out of the students who play an instrument, 40% play the piano. What is the probability that a randomly chosen student from the school plays the piano?