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

Result Not Found

Books FREE
Study Help
Tutors
AI Study Planner NEW
Sell Books

Search
Sign In
Register

study help
business
probability statistics

Probability Statistics And Stochastic Processes For Engineers And Scientists 1st Edition Aliakbar Montazer Haghighi ,Indika Wickramasinghe - Solutions

Suppose a particular examination that is needed to enter to a graduate school has a normal distribution with a mean of 150 and a standard devia-tion of 10. Considering a student is going to take this examination, i. What is the probability that his score is between 145 and 160?ii. What is the
Let X be a continuous random variable with pdf f()xx=−1−1, 02≤≤x.i. Find cdf of X and graph it.ii. Find the first decile.iii. Find 20th and 95th percentiles, and show them on the graph of cdf of X.iv. Find the IQR.
Suppose a random variable X has a uniform distribution over [,ab], where 0≤
Suppose a random variable X has a uniform distribution over [1,β] for some β>1. Calculate the value of β if PX(2
Consider a layer of a particular paint applied on metal surfaces to protect from corrosion. Assume that the thickness of the above paint has a uniform distribution, which is distributed between 10 and 20 μm. If a metal surface with this paint is randomly selected, i. What is the expected value of
The error in the reaction time X (in minutes) of a certain machine has the following distribution:i. Construct the cdf of X.ii. What is the probability that the error in the reaction time is over 0.5?
Note that the pH value of a soil in a certain area has the following distrib-uted function:i. Calculate the constant k.ii. What is the mean pH value of this soil?iii. If a soil sample from this area is selected, what is the probability that the pH value of the soil is more than 5?
Consider the following joint pmf of X and Y.i. Construct the marginal pmf of X and Y.ii. Calculate the expected values and the variances of X and Y.iii. Calculate the covariance of X and Y.iv. Calculate the coefficient of correlation. Y = 0 Y = 1 Y = 2 X=0 0.3 0.2 0.1 X=1 0.2 0.1 0.1
Assume that the number of bacterial colonies of a certain type is grown at a rate of 2 colonies per minute. Assume that two or more colonies do not grow at the same time, and they are independent. Considering a 5-minute period, i. What is the probability that no more than 15 colonies are grown
A service station experiences ten vehicles arriving in an hour. Assume that the arrival of vehicles is independent and no more than one vehicle arrives at the same time. Considering a particular hour at the service station, i. What is the probability that there are at most five vehicles arriving to
Let us suppose that sale of a flood insurance by a salesperson is according to a Poisson pmf, with an average of 3 per week. Use Poisson pmf to calcu-late the probability that in a given week the salesperson will sell i. Some policies.ii. Two or more policies but less than five policies.iii.
The number of telephone calls receiving per 5 minutes to a hotel’s reservation center follows a Poisson random variable with a mean of 3. Find the probability that no call is received by the hotel in a given 5-minute period.
Assume that there is a 10% chance a certain baseball player hits a home run in a game. What is the probability that the player completes his second home run in his fifth game?
Consider a particular type of lottery with 2% chance of winning any kind of prize. Suppose a person wants to buy this lottery until he wins a prize. What is the probability that he gets his first win from the fifth lottery he purchases?
Usually a particular type of candy bags contains ten candies in each bag. Only 20% of the candy bags contains 15 candies in the candy bag. Suppose a kid is trying to find a bag with 15 candies. How many candy bags does he needs to open until he finds the first bag with 15 candies?
Suppose 10% of the drivers in a particular city do not possess a valid driver’s license. A traffic inspector is inspecting all the drivers coming to a particular junction in this city. What is the probability that the inspector needs to inspect five drivers until he finds the first driver without
A quality controller knows by his experience that 10% of the items he inspects are defective. He randomly selects 30 items from the production and wants to inspect them.i. Calculate the expected number of defective items he is going to find.ii. What are the variance and the standard deviation of
A clothing store has determined that 30% of the customers who enter the store will use a Visa credit card. Consider a collection of 15 customers who have entered to the store.i. How many of them you expect to use Visa card?ii. What is the probability that more than five customers use Visa card?
A laboratory network consisting of 25 computers was attacked by a c omputer virus. This virus enters each computer with a probability of 0.4, independently of other computers. What is the probability that i. At least ten computers are affected by the virus?ii. More than ten computers are affected
An examination consists of 20 multiple-choice questions. Suppose each question has four possible choices, but only one of them is the correct solu-tion. If a student who did not study for the examination is going to guess at the examination, what is the probability that he guesses i. Exactly five
Consider a bicycle seller, who purchases a batch of five bicycles from a company and sells to customers. He buys these bicycles from the com-pany for $100 per bicycle and sells one for $150. According to his experi-ence, he knows that he has 1% chance not to sell any bicycle, 5% chance to sell one
Suppose an individual plays a gambling game where it is possible to lose $1.00, break even, win $3.00, or win $10.00 each time she plays. The prob-ability distribution for each outcome is provided by the following table:Calculate the expected value and the variance of the amount an indi-vidual
Consider a random variable with the following probability mass function x = 1,2,3 (pmf): P(x)= where k is a positive constant. 0; else i. Calculate the constant k. ii. Construct the cumulative distribution function (cdf) of the random variable.
Suppose the number of years of experience (X) an employee possesses when joining to a particular type of job is given by the following pmf:i. Calculate the expected number of years of experience a new employee possesses when joining to the above job.ii. What is the probability that a new employee
Let X represent the number of months between two power outages that occur. The cumulative probability distribution of X is as follows:i. Construct the pmf of X.ii. What is the expected number of months between two successive power outages?iii. What is the probability of the number of months between
A sample of 100 married women was taken. Each was asked how many children she had. Responses were tallied as follows:i. Find the average number of children in the sample.ii. Find the sample standard deviation of the number of children.iii. Find the sample median.iv. What is the first quartile of
A particular gas station has five gas pumps. Let Y denote the number of gas pumps that are in use at a specified time. Consider the following pmf of Y.Calculate the probability of each of the following events.i. {at most 3 pumps are in use}, ii. {fewer than 3 pumps are in use}, iii. {at least 3
Consider the probability distribution of the random variable X.i. Construct the probability distribution X in the tabular form.ii. Calculate the expected value of X. Px(x) 0.3 0.2 0.1 0 1 2 3 4 5
A computer vender knows the following information by his experience. 20% of the time he does not sell any computer, 35% of the time he sells one computer, 25% of the time he sells two computers, and 20% of the time he sells three computers. Taking the number of computers the vender sells as the
Consider the probability distribution of the random variable X.i. Complete the above table.ii. What is the most likely occurring value of the random variable X?iii. Compute PX(3iv. Compute PX(2≤).v. Compute PX(3>).vii. Compute PX(1vi. Compute PX(1 X 0 1 2 3 4 p(x) 0.2 0.3 0.1 0.2
Assume you examine three bicycles reaching to a junction. You are going to observe whether the bicycles are going straight (0), turn to left (−1), or turn to right (1) from the junction. Let X be the random variable that represents the sum of the values assigned to each direction of the above
Consider the experiment of rolling two dice and the following random variables.Let W = The sum of the two numbers that appear on two dice.X = The absolute value of the difference of two numbers that appear on two dice.Y Both numbers that appear are the same. =i. State the possible values of each of
Prove the generalization of the multiplicative law: For n events E12,,EE...,n with nonempty intersections, prove the multiplication law with conditional probability: P(EE..E) = P(E)P(E|E)P(E3|EE)...P(EEE...En-1).
Prove the distributive laws of probability.i. Let E12,,E... be any events. Then, we have the following two properties:ii. For a finite number of events Ej,1jn=,2,...,, prove the following:iii. For an infinite number of events Ej,1jn=,2,...,, prove the following: a. (UE) A=U(EA) b. (DE)UA=(EUA)
Let E1 and E2 be two events in the space ????. The following are some proper-ties of the probability measure P. Prove the following:If E1 and E2 are two events in ???? and P is a probability measure, then P is a monotonic function, that is, i. PE()12≤PE(),ifE1E2⊂ii. P(E1c ) = 1− P(E1 )iii.
There are three brands of soda, say A, B, and C, available in a store. Assume that 40%, 35%, and 25% of the soda drinkers prefer brands A, B, and C, respectively. When a brand A soda drinker is considered, only 30% of them use ice cubes to drink the soda. For brands B and C, these percentages are
A group of students comprise 30% biology majors, 25% math majors, and 45% engineering majors. Suppose that GPA of 30% of mathematics and biology majors is above 3.0 out of 4.0 points. For mathematics and engi-neering students, the numbers are 40% and 30%, respectively. Answer the following
Let A be the event that a person drives an automatic-geered car, and B be the event that the person drives a manual-geered car. Suppose PA()=0.5, PB()=0.4, and PA()∩=B0.25.i. Interpret the event BA and calculate its probability.ii. Interpret the event AB and calculate its probability.
A survey was conducted about the three hobbies, namely, reading books, watching movies, and listening to music. The following statistics were cal-culated using a collection of 1,000 college students. Of them, 13%, 22%, and 36% read books, watch movies, and listen to music, respectively. Also, 7% of
It is known that 10% of new computers arriving at a computer store are defective of some type. Answer the following questions:i. Two computers of some new arrivals have been selected consecutively to check for defectiveness without replacement. What is the probabil-ity that the first computer is
Consider two events A and B with PA()B=0.6 and PB()=0.5. Calculate PA()∩B.
Answer the follow-ing questions:i. What is the probability that both of motorcycles have mechanical problems?ii. What is the probability that either Steve’s or his sister’s motorcycle has a mechanical problem?iii. What is the probability that only one of the motorcycles has a mechan-ical
Suppose Steve and his sister have motorcycles. The probability that Steve’s cycle has a mechanical problem is found to be 0.3, whereas the probability that his sister’s cycle has a mechanical problem is
According to the estimation of a particular insurance company, in a par-ticular year, 1 out of each 300 houses can experience fire at some point of time. If there are eight houses with insurance protection for fire, what is the probability that the insurance company needs to pay for all the eight
At a small college, 10% of the students are mathematics majors. Answer the following questions:i. If a student is selected at random from this college, what is the prob-ability that the student is not a mathematics major?ii. If three students are randomly selected, what is the probability that all
In an experiment of rolling two fair dice simultaneously, what is the prob-ability that both show 5?
In addition, the quality controller finds that all the three types of defects occur 1% of the time. Using this informa-tion, answer the following questions:i. What is the probability that the quality controller experiences any type of defects?ii. What is the probability that the quality controller
A quality controller finds three types of defects with a particular product in a company. Based on her experiences, she expects percentages of these defects as 7, 8, and 9, for type 1, 2, and 3 defects, respectively. Also, the probability of defects for both types 1 and 2 is 0.03, for types 2 and 3
A mechanic shop has three mechanics, identified as #1, #2, and #3. The per-centage of all jobs assigned are 40, 35, and 25, to mechanics #1, #2, and #3, respectively. From the history of experience, the owner of the shop knows the probability of errors for each of the mechanics as 0.05, 0.03, and
Consider the results of a survey conducted by a researcher regarding the owning of the latest smart phones. This study was conducted using a group of high school students.If a student is randomly selected, calculate the probabilities of the fol-lowing events:i. The student is a male.ii. The student
Consider a shipment of computers to an electronic store. Historical data indicates that a shipment of this type contains defects of different types. Here are the numbers: CPU only: 5%, RAM: 7%, and both CPU and RAM: 3%. To assess the defectiveness, a computer is selected randomly. Find the
A bookstore carries some academic books, including mathematics and biology. The kind of books purchased are noted. Let us focus on the next customer who is at the register and is buying books. A denotes the event that the customer purchases a mathematics book, and B denotes the event that the
A professor in a college posted the following grade distribution for one of his courses he teaches,with “D” to be considered as failure grade. If a student is selected ran-domly, find the probability of the following events:i. The student received a grade higher than a “C”.ii. The student
There are 100 mathematics majors and 200 engineering majors in a group of 500 students. If a student is randomly selected, answer the following questions:i. What is the probability that the student is not an engineering major?ii. What is the probability that the student is a mathematics major?iii.
Suppose there is an urn with 20 equal-sized balls. Of them, 12 are red, 5 are blue, and the rest are of different colors. If you randomly select a ball, what is the probability that the ball picked i. Is red?ii. Is neither red nor blue?
Consider a standard deck of 52 playing cards. Randomly select a card. What is the probability that thei. Card is a queen?ii. Card is a queen and a spade?iii. Card is a queen or a spade?iv. Card is a queen but not a spade?
What is the sample space when measuring the lifetime of a light bulb?
To assess the quality of a certain product of a company, the controller of the company uses a sample of size 3. His choices for rating are as follows:i. Above the average, ii. Average, iii. Below the average.Answer the following questions:a. State the sample space of the rating.b. Define an event
A pair of two fair dice is rolled and the outcomes are observed.i. State the sample space for the experiment.ii. Define an event that represents the sum of two numbers is 5. Find the probability of this event.iii. Define an event that represents the absolute value of the difference is 1. Find the
State the sample space when a coin and a die are tossed together.
Consider an experiment of observing the gender of a child of a family of three children.i. State the sample space.ii. Define an event as a family with only one boy. State the sample points for this event.
Consider an experiment of tossing two fair coins. Suppose you observe two outcomes of both coins. State the sample space.
Suppose it is known that a box of 24 light bulbs contains five defective bulbs. A customer randomly chooses two bulbs from the box without replacement.i. What is the total number of ways the customer can choose the bulbs?ii. What is the number of ways to choose no defective bulb?
Consider the set {1,2,3}.i. Write the elements of the permutations by taking two digits from above three ii. Write the elements of the permutation without repetition of the 3 numbers taken all 3 at a time.iii. Do both cases (i) and (ii) have the same number of elements?
Using the Stirling formula, approximate the error of calculating 2! (2 factorial).
Suppose we are to create 6-character codes (xxxxxx) for products of a manufacturer. The characters in each code are to be:A letter,Another letter different from the first choice,Another letter different from the first two choices,A nonzero digitTwo digits.How many different codes could we have?
Suppose a company is to establish an Executive Committee consisting of two men and three women. There is a pool of ten candidates consisting of six men and four women. In how many ways can this committee be established?
Suppose stocks of eight electronic items and five real estate buildings are available in the stock market. We want to create a stock shares portfolio with four electronic items and three real estate pieces. How many different ways can we form this portfolio?
An executive lady has four clean skirts and five clean blouses to wear to work in a certain week. How many ways can she choose outfits for Monday, Wednesday, and Friday if i. She does not wish to wear the same skirt or blouse twice?ii. She is willing to repeat her attire?iii. She is willing to
Three cars enter a parking lot with 11 empty parking spaces. Each car has an option of backing into its parking space or driving in forward. How many ways can the three drivers select i. Parking spaces?ii. Parking spaces and parking positions?
Fifteen planes are commuting between two cities A and B. In how many ways can a person go from A to B and return by a different plane?
In how many ways can a group of five girls and two boys be made out of a total of seven boys and three girls?
In how many different ways can the letters of the word “MATHEMATICS” be arranged so that the vowels always come together?
In an election of the Student Government Association Executive Committee at a university, there are 13 student candidates, with 7 females and 6 males. Five persons are to be selected that include at least 3 females. In how many different ways can this committee be selected?
A game team consists of ten players, six male and four female players. In how many different ways can four players be selected such that at least one male player is included in the selected group?
Find the number of ways of choosing 2 consonants from 7 and 2 vowels from 4.
Let A={0,3,6,9} and B={1,2,4,7,8}. Draw the Venn diagram illustrating these sets with the union as the universal set.
In a group of musicians, including singers, if S is the set of singers and I is the set of instrumentalists, in a set notation, i. Write the set of singers who play an instrument.ii. Write the set of musical performers.
Considering the set E of English alphabets, if V is the set of vowels, what is the complement of V called?
For A={2,4,5} and B={3,4,5}, answer the following questions:i. Is A a subset of B?ii. Is B a proper subset of A?iii. Find the intersection of A and B.
Determine if the set is finite or infinite, and justify your answer:i. The set of whole numbers between 1 and 10.ii. The set of positive real numbers less than 9.iii. The set of natural numbers greater than 9.iv. The set A={3,6,9,12,...}.
List the elements of a set A containing natural numbers between 20 and 200, divisible by 4.
Let us denote a rainy day by R, a windy day by W, and a sunny day by S. Let E be the set of days in September. Draw a Venn diagram, if in Houston Texas in a September month, there are, on the average, 15 sunny days, 5 windy days, and 18 rainy days.
A mathematics department has 40 full-time faculty members. For profes-sional development and service to the profession, each may belong to one or more mathematics professional organizations such as 1. AMS (American Mathematical Society), 2. SIAM (Society for Industrial and Applied Mathematics), 3.
How many elements are in the set {1,a, 2,1,a}?
Are {1,3,4} and {4,3,1,1} equal sets?

Showing 8600 - 8700 of 8686

First
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87

Step by Step Answers

Services

Sitemap
Fun
Definitions
Become Tutor
Used Textbooks
Study Help Categories
Recent Questions
Expert Questions
Campus Wear
Sell Your Books

Company Info

Security
Copyrights
Privacy Policy
Terms & Conditions
SolutionInn Fee
Scholarship
Online Quiz
Give Feedback, Get Rewards

Get In Touch

About Us
Contact Us
Career
Jobs
FAQ
Student Discount
Campus Ambassador

Secure Payment

Download Our App

© 2026 SolutionInn. All Rights Reserved