New Semester
Started
Get
50% OFF
Study Help!
--h --m --s
Claim Now
Question Answers
Textbooks
Find textbooks, questions and answers
Oops, something went wrong!
Change your search query and then try again
S
Books
FREE
Study Help
Expert Questions
Accounting
General Management
Mathematics
Finance
Organizational Behaviour
Law
Physics
Operating System
Management Leadership
Sociology
Programming
Marketing
Database
Computer Network
Economics
Textbooks Solutions
Accounting
Managerial Accounting
Management Leadership
Cost Accounting
Statistics
Business Law
Corporate Finance
Finance
Economics
Auditing
Tutors
Online Tutors
Find a Tutor
Hire a Tutor
Become a Tutor
AI Tutor
AI Study Planner
NEW
Sell Books
Search
Search
Sign In
Register
study help
business
elementary probability for applications
Probability An Introduction With Statistical Applications 2nd Edition John J Kinney - Solutions
A square law rectifier has the characteristic Y = kX2, x > 0, where X and Y are the input and output voltages, respectively. If the input to the rectifier is noise with the probability density functionfind the probability density function of the output. f(x) = x/p, x0, p>0,
Suppose that X1 is the number of 6’s in n1 tosses of a fair die and that Y is the number of 3’s in n2 tosses of another fair die. Use moment generating functions to show that S = X + Y has a binomial distribution with parameters n = n1 + n2 and p = 1∕6.
A random variable has M[X; t] = 2 5et + 1 5e2t + 2 5e3t .(a) What is the probability distribution function for X?(b) Expand M[X; t] in a power series and find ????x and ????2 x .
Find the moment generating function for a random variable X with probability density function f (x) = e − ex if 0 ≤ x ≤ 1.
A discrete random variable X has the probability distribution function f(x)= 121396 x=1 x=2 x = 3. (a) Find and . (b) Find M[X;t]. (c) Verify the results in part (a) using the moment generating function.
A random variable X has M[X; t] = e−6t+32t2. Find P(−4 ≤ X ≤ 16).
A random variable X has the probability density function f (x) = 2(1 − x), 0 < x < 1.(a) Find the moment generating function for X.(b) Use the moment generating function to find a formula for E(Xk).(c) Let Y = 1 2 (X + 1). Find M[Y; t].
A random variable X has the probability distribution function f (x) = 1 3for x = −1, 0, or 1.(a) Find M[X; t], the moment generating function for X.(b) If X1 and X2 are independent observations of X, find M[X1 + X2; t] without first finding the probability distribution of X1 + X2.(c) Verify the
The time a construction crew takes to construct a building is normally distributed with mean 90 days and standard deviation 10 days. After construction, it takes additional time to install utilities and finish the interior. Assume the additional time is independent of the construction time, and is
A student makes 100 check transactions in a period covering his bank statement.Rather than subtract the amount he spends exactly, he rounds each checkbook entry off to the nearest dollar. Assume that the errors are uniformly distributed on[−1 2, 1 2].What is the probability the total error is
Mathematical and verbal SAT scores are, individually, N(500, 100).(a) Find the probability that the total mathematical plus verbal SAT score for an individual is at least 1100, assuming that the scores are independent.(b) What is the probability that the average of five individual total scores is
Suppose 12 fair dice are thrown. Let X denote the total number of spots showing on the 12 uppermost faces. Use the central limit theorem to estimate P(25 ≤ X ≤ 40).
A sample of size n is drawn from a population about which nothing is known except that the variance is 4. How large a sample must be drawn so that the probability is at least 0.95 that the sample average, X, is within 1 unit of the true population mean, ?????
A company claims that the actual resistance of resistors are normally distributed with mean 200 ohms and variance 4 ⋅ 10−4 ohms2.(a) What is the probability that a resistor drawn at random from this set of resistors will have resistance greater than 200.025 ohms?(b) A sample of 25 resistors
Customers at a gasoline station buy regular or premium unleaded gasoline with probabilities p and q = 1 − p, respectively. The number of customers in a daily period is Poisson with mean ????. Find the probability distribution for the number of customers buying regular unleaded gasoline.
The coin loaded so as to come up heads 1/3 of the time is tossed until a head appears.This is followed by the toss of a coin loaded so as to come up heads with a probability of 1/4 until that coin comes up heads.(a) Find the probability distribution of Z, the total number of tosses necessary.(b)
A fair quarter is tossed until it comes up heads; suppose X is the number of tosses necessary. If X = x, then x fair pennies are tossed; let Y denote the number of heads on the pennies. Find P(Y = 3), simplifying the result as much as you can.
Let S =Σn i=1 Xi, where Xi is a uniform random variable on the interval (0,1). Find the moment generating function for Z = S−????????where ???? and ???? are the mean and standard deviation, respectively, of S. Then show that this moment generating function approaches the moment generating
Find E(Xk) if X is a Weibull random variable with parameters ???? and ????.
Random variable X denotes the number of green marbles drawn when a sample of two is selected without replacement from a box containing 3 green and 7 yellow marbles.(a) Find the moment generating function for X.(b) Verify that E(X3) = 1.
Consider the truncated exponential distribution, f (x) = ex, 0 ≤ x ≤ ln 2.(a) Find the moment generating function for X and expand it in a power series.(b) From the series in part a], find the mean and variance of X.
Find the mean and variance of X where X has the Pareto distribution, f (x) = a ⋅ ba ⋅x−(a+1), a > 0, b > 0, x > b.
For the triangular distribution f (x) = 2 a(1 − x a), 0 < x < a,(a) Find the moment generating function.(b) Use the moment generating function to find the mean and variance of X and check these results by direct calculation.
One hundred independent observations are made of the random variable X whose probability density function isFind the probability that at least 20 of these observations exceed 1.5. x 0 x 1 f(x) = 2-x 1x2.
The time (in seconds) a car has to wait for a certain traffic light has probability density function(a) What is the probability that the waiting time is between 25 and 75 seconds?(b) If a car haswaited 25 seconds, what is the probability it willwait at least 25 seconds more? f(x)= x 2500 0x50 x 50
(a) Determine k so that f (x) = kxe−x2 is a probability density function for some nonnegative random variable X.(b) Determine F(x) and sketch it.
A random variable X has probability density functionFind E[X2 − 2X + 2]. f(x)= 1+x-1
Find the mean and variance of the random variable X whose probability density function is f(x) = (1-x)(x-3), 1x3. 4
Suppose X has the distribution function (a) Find a. (b) Find P(X1). 0 x
Verify Tchebycheff’s inequality for k =√2 for the probability density function f(x)=(x+1), -1
A random variable, X, has probability density function (a) Show that a = == (b) Find P(X4). f(x)= ax 0x 3 6a-ax 3x 6.
A point B is chosen at random on a line segment AC of length 10. A right-angled triangle with sides AB and BC is constructed. Determine the probability that the area of the triangle is at least 7 square units.
Suppose that f (x) = 3x2, 0 < x < 1, is the probability density function for some random variable X. Find P(X ≥ 1 2|||X ≥ 1 4).
The percentage, X, of antiknock additive in a particular gasoline, is a random variable with probability density function(a) Show that k = 20.(b) Evaluate P[X (c) Find F(x). f(x)=kx(1-x), 0
Let X be a random variable with probability density function(a) Find k.(b) Calculate E(X).(c) Find the cumulative distribution function, F(x). f(x)= k 1x2 k(3-x) 2x3. |k (3 - x)
Students in an electrical engineering laboratory measure current in a circuit using an ammeter. Due to several random factors, the measurement, X, follows the probability density function f (x) = 0.025 x +b, 2 < x < 6.(a) Show that b = 0.15.(b) Find the probability the measurement of the current
The length of life in hours, X, of an electronic component has an exponential probability density function with mean 500 hours.(a) Find the probability that a component lasts at least 900 hours.(b) Suppose a component has been in operation for 300 hours. What is the probability it will last for
A sugar refinery has three processing plants, all receiving raw sugar in bulk. The amount of sugar in tons that each of the plants can process in a day has an exponential distribution with mean 4.(a) Find the probability a given plant processes more than 4 tons in a day.(b) Find the probability
The weights of oranges in a good year are described by a normal distribution with???? = 16 and ???? = 2 (ounces).(a) What is the probability that a randomly selected orange has weight in excess of 17 ounces?(b) Three oranges are selected at random. What is the probability the weight of exactly one
The annual rainfall (in inches) in a certain region is normally distributed with ???? =40, ???? = 4. Assuming rainfalls in different years are independent, what is the probability that in 2 of the next 4 years the rainfall will exceed 50 inches?
Manufactured parts have lifetimes in hours, X, that are distributed N(1000, 100). If 800 ≤ X ≤ 1200, the manufacturer makes a profit of $50 per part. If X > 1200, the profit per part is $75; otherwise, the manufacturer loses $25 per part. What is the expected profit per part?
A buyer requires a supplier to deliver parts that differ from 1.10 by no more than 0.05 units. The parts are distributed according to N(1.12, 0.03).What proportion of the parts do not meet the buyer’s specifications?
Electric cable is made by two different manufacturers, each of whom claims that the diameters of their cables are normally distributed. The diameters, in inches, from Manufacturer I are N(0.80, 0.02) while the diameters from Manufacturer II are N(0.78, 0.03). A purchaser needs cable that has
A machining operation produces steel shafts having diameters that are normally distributed with mean 1.005 inches and standard deviation 0.01 inches. If specifications call for diameters to fall in the interval 1.000±0.02 inches, what percentage of the steel shafts will fail to meet specifications?
Ten people are wearing badges numbered 1, 2, … 10. Three people are asked to leave the room. What is the probability that the smallest badge number among the three is 5?
Let X be Poisson with parameter ????.(a) Find a recursion for P(X = x + 1) in terms of P(X = x).(b) Use the recursion in part (a) to find ???? and ????2.
Calls come into an office according to a Poisson process with 3 calls expected per hour.Suppose that the calls are answered independently, with the probability that a call is answered as 3/4. Find the probability that exactly 4 calls are answered in a 1-hour period.
(a) Suppose that X is a Poisson random variable with parameter ????. Find ???? if P(X = 2) = P(X = 3).(b) Show if X is a Poisson random variable with parameter ????, where ???? is an integer, then some two consecutive values of X have equal probabilities.
Three fair dice are rolled. You as the bettor are allowed to bet $1 on the occurrence of one of the integers 1, 2, 3, 4, 5, or 6. If you bet on X and X occurs k times (k = 1, 2, 3), then you win $k; otherwise, you lose the $1 you bet. Let W represent the net winnings per play.(a) Find the
Three marbles are drawn without replacement from a bag containing three white, three red, and five green marbles. $1 is won for each red selected and $1 is lost for each white selected. No payoff is associated with the green marbles. Let X denote the net winnings from the game. Find the probability
How large a sample is necessary to estimate the proportion of people who do not know whose picture is on the $1 bill to within 0.02 with probability 0.90?
A survey of 400 children showed that 1/8 of them were on welfare. Find a 95% confidence interval for the true proportion of children on welfare.
The Internal Revenue Service says that the chance a United States Corporation will have its income tax return audited is 1 in 15. A sample of 75 corporate income tax returns showed that 6 were audited. Does the data support the Internal Revenue Service’s claim? Use ???? = 0.05.
A management study showed that 1/3 of American office workers has his or her own office while 1/33 of Japanese office workers has his or her own office. The study was based on 300 American workers and 300 Japanese workers. Could the difference in these proportions only be apparent and due to
A survey of 300 workers showed that 100 are self-employed. Find a 90% confidence interval for the proportion of workers who are self-employed.
Jack thinks that he can guess the correct answer to a multiple choice question with probability 1/2. Kaylyn thinks his probability is 1/3. To decide who is correct, Jack takes a multiple choice test, guessing the answer to each question. If he answers at least 40 out of 100 questions correctly, it
A drug is thought to be effective in 10% of patients with a certain condition. To test this hypothesis, the drug is given to 100 randomly chosen patients with the condition. If 8 or more show some improvement, Ho∶ p = 0.10 is accepted; otherwise, Ha∶ p < 0.10 is accepted. Find the size of the
A study of 1200 college students showed that 44% of them said that their political views were similar to those of their parents. Find a 95% confidence interval for the true proportion of college students whose political views are similar to those of their parents.
In problem 28, find the size of ???? for the alternative p = 0.72.
Past studies have shown that 2/3 of professional football players will sustain a permanent injury before retiring. To see if this proportion is true for current players, a sample of 100 retired professional football players showed that 80 of them had sustained permanent injuries. Using ???? = 0.05,
A machine, producing defective parts with probability 1/10, has produced five parts.Unknown to the operator of the machine, an adjustment to the machine increases this probability to 1/5. Ten parts are produced after the adjustment. What is the probability the output contains at least 2 defectives?
A player pays $A to play the following game: a coin, loaded to come up heads with probability 2/3, is tossed five times. Let X denote the number of heads. The player wins$(X + 1) if X is even and wins $(X − 1) if X is odd. Find A so that the game is fair.
A tosses three coins that have probability pA of coming up heads while B tosses two coins that have probability pB of coming up heads.(a) Find an expression for the probability that A tosses more heads than B.(b) Show that the game is fair if the coins are fair.
A box contains three blue and four yellow marbles. Marbles are drawn out one at a time, the drawn marbles not being replaced. Drawings are made until all the marbles remaining in the box are of the same color.(a) Assign probabilities to the sample points and verify that their sum is 1.(b) What is
A box contains 4 bad and 6 good tubes. The tubes are checked by drawing a tube at random and not replacing it in the box. In how many ways can the fourth bad tube be found on the seventh drawing?
Telephone calls come into an answering service at an average rate of 3 per hour, the number of calls following a Poisson distribution. During the noon hour, only the first 3 calls are answered. What is the expected number of calls answered during the noon hour?
A pair of fair dice is rolled 180 times each hour in a dice game at a casino. What is the probability that at least 25 rolls give a sum of 7 during 1 hour?
Fifty chocolate chip cookies are to be made using 150 chocolate chips. The number of chocolate chips per cookies is a Poisson random variable.(a) What is the probability a cookie has at least 4 chocolate chips?(b) How many chocolate chips must be used in order to make the probability a cookie has
Customers arrive at a computer store according to a Poisson process with 5 customers expected per hour. The sales force can accommodate at most 10 customers per hour; if more than 10 customers appear in an hour, the excess must be turned away.(a) What is the probability that customers are turned
From a lot of 25 items, 5 of which are defective and 4 are chosen at random. Let X be the number of defectives found. Find the probability distribution of X if(a) 1. the items are chosen with replacement.2. the items are chosen without replacement.(b) In part (a) assume that the items are chosen
A fair die is tossed until a 5 or a 6 appears. Compute the probability that the number of tosses is a multiple of 4.
Thirty percent of the applicants for a position have advanced training in computer programming.Three jobs requiring advanced training are open. Find the probability that the third qualified applicant is found on the fifth interview, supposing that the applicants are interviewed sequentially and at
A manufacturer produces items that are good or defective, according to a binomial process where p is the probability an item is defective. Let X denote the number of items produced up to and including the second defective item.(a) Find an expression for the probability that X is even.(b) Now
Customers arrive at a checkout counter in a supermarket at a rate of 20 per half hour, the number following a Poisson distribution. What is the probability that at most 5 customers arrive in a period of 15 minutes?
In a small voting precinct, 100 voters favor candidate A and 80 voters oppose candidate A. What is the probability that a majority of a random sample of 4 voters will oppose candidate A?
Errors are known to occur in a digitized message in a communications channel; the probability an individual bit is incorrectly transmitted is 0.001 and the errors are assumed to be independent.(a) Find the probability that at most 2 errors occur in a sequence of 10 bits.(b) Find the mean and
Five defective transistors are mixed up with 10 good transistors. They are inspected one after another until all the good transistors have been found. What is the probability the last good transistor will be found on the 12th test?
A store sells chocolate donuts at a rate of 16 per hour, the number sold following a Poisson distribution. Find the probability that the store sells at least 3 chocolate donuts in 15 minutes.
(a) What is the probability that a poker hand contains exactly 2 aces?(b) How many poker hands must be selected to make the probability of having at least one hand containing at least 2 aces be at least 0.99?
A manufacturer makes a lot of 10 items a day. Two items are drawn (without replacement)and inspected. The lot is accepted if the sample contains at most 1 defective item.Find the probability a lot containing 3 defective items is accepted.
A series of trials in which success or failure occurs on each trial has probability of success at the ith trial as 1 i+1. In three trials, find the probability of exactly 2 successes.
Suppose that X and Y are independent observations of a Poisson random variable with parameter ???? = 1. Find the probability that the smallest of the two observations is 1.
Suppose an event has probability p of occurring and that several independent trials are observed. What value of p maximizes the probability that the first failure occurs on the fifth trial?
Earthquakes in a certain part of California occur according to a Poisson process with three earthquakes expected each century.(a) What is the probability of exactly four earthquakes in a century?(b) What is the probability of at least two earthquakes in a 50-year period?(c) Let X be the number of
A manufacturer of soft drink bottles turns out defectives with probability 0.10. Assume that the bottles are produced according to a binomial process.(a) Find the probability that there are 4 defective bottles among the next 10 bottles produced.(b) Find the probability that there are at least 4
Twenty percent of the IC chips made in a plant are defective. Assume that the chips are produced according to a binomial process.(a) Find the probability that at most 13 defectives occur in a sample of 100 IC chips.(b) Approximate the probability in part (a) by a Poisson random variable.
Calls come into a telephone exchange at a rate of 1.5 per minute. Assuming that the number of calls received follows a Poisson distribution, find the probability that at least==3 calls are received in the next 4 minutes.
Independent events A and B have probabilities pA and pB, respectively. Show that the probability of either two successes or two failures in two trials has probability 1/2 if and only if at least one of pA and pB is 1/2.
A recent issue of a newspaper said that given a 5% probability of an unusual event in a 1-year study, one should expect a 35% probability in a 7-year study. This is obviously faulty. What is the correct probability?
A production lot has 100 units of which 25 are known to be defective. A random sample of 4 units is chosen without replacement. What is the probability that the sample will contain no more than 2 defective units?
In how many different ways can n people be seated around a circular table?
A box contains tags numbered 1, 2, ..., n. Two tags are chosen without replacement.What is the probability they are consecutive integers?
Find the probability a poker hand contains 3 of a kind (exactly 3 cards of one face value and 2 cards of different face values).
A “rook” deck of cards consists of four suits of cards: red, green, black, and yellow, each suit having 14 cards. In addition, the deck has an uncolored “rook” card. A hand contains 14 cards.(a) How many different hands are possible?(b) How many hands have the rook card?(c) How many hands
A roulette wheel has 38 slots—18 red, 18 black, and 2 green (the house wins on green).Suppose the spins of the wheel are independent and that the wheel is fair. The wheel is spun twice and we know that at least one spin is green. What is the probability that both spins are green?
An inexperienced employee mistakenly samples n items from a lot of N items, with replacement. What is the probability the sample contains at least one duplicate?
The probability is 1 that a fisherman will say he had a good day when, in fact, he did, but the probability is only 0.6 that he will say he had a good day when, in fact, he did not. Only 1/4 of his fishing days are actually good days. What is the probability he had a good day if he says he had a
A pair of dice is rolled until a 5 or a 7 appears. What is the probability a 5 occurs first?
Three integers are selected at random from the set {1, 2, … , 10}. What is the probability the largest of these is 5?
A box contains slips of paper numbered from 1 to m. One slip is drawn from the box;if it is 1, it is kept; otherwise, it is returned to the box. A second slip is drawn from the box. What is the probability the second slip is numbered 2?
Showing 200 - 300
of 3340
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Last
Step by Step Answers
Get 50% OFF
Claim Now
