A First Course in Probability (10th Edi...10th EditionSheldon Ross Publisher: PEARSONISBN: 9780134753119
A First Course in Probability (10th Edi...
Solutions for A First Course in Probability (10th Edition)
Problem 4.1P:
Two balls are chosen randomly from an urn containing 8 white, 4 black, and 2 orange balls. Suppose...Problem 4.2P:
Two fair dice are rolled, Let X equal the product of the 2 dice. Compute P{X=i} for i=1,...,36.Problem 4.3P:
Three dice are rolled. By assuming that each of the 63=216 possible outcomes is equally likely, find...Problem 4.4P:
Five men and 5 women are ranked according to their scores on an examination. Assume that no two...Problem 4.5P:
Let X represent the difference between the number of heads and the number of tails obtained when a...Problem 4.6P:
In Problem 4.5 for n=3, if the coin is assumed fair, what are the probabilities associated with the...Problem 4.7P:
Suppose that a die is rolled twice. What are the possible values that the following random variables...Problem 4.8P:
If the die in Problem 4.7 is assumed fair, calculate the probabilities associated with the random...Problem 4.12P:
In the game of Two-Finger Morra, 2 players show 1 or 2 fingers and simultaneously guess the number...Problem 4.13P:
A salesman has scheduled two appointments to sell vacuum cleaners. His first appointment will lead...Problem 4.14P:
Five distinct numbers are randomly distributed to players numbered 1 through 5. Whenever two players...Problem 4.15P:
The National Basketball Association (NBA) draft lottery involves the 11 teams that had the worst...Problem 4.16P:
A deck of n cards numbered 1 through n are to be turned over one a time. Before each card is shown...Problem 4.17P:
Suppose that the distribution function of X is given byF(b)={0b0b40b112+b141b211122b313b a. Find...Problem 4.18P:
Four independent flips of a fair coin are made. Let X denote the number of heads obtained. Plot the...Problem 4.19P:
If the distribution function of X is given byF(b)={0b0120b1351b2452b39103b3.51b3.5 calculate the...Problem 4.20P:
A gambling book recommends the following winning strategy for the game of roulette: Bet $1 on red....Problem 4.21P:
Four buses carrying 148 students from the same school arrive at a football stadium. The buses carry,...Problem 4.22P:
Suppose that two teams play a series of games that ends when one of them has won i games. Suppose...Problem 4.23P:
You have $1000, and a certain commodity presently sells for $2 per ounce. Suppose that after one...Problem 4.24P:
A and B play the following game: A writes down either number 1 or number 2, and B must guess which...Problem 4.26P:
One of the numbers I through 10 is randomly chosen. You are to try to guess the number chosen by...Problem 4.27P:
An insurance company writes a policy to the effect that an amount of money A must be paid if some...Problem 4.28P:
A sample of 3 items is selected at random from a box containing 20 items of which 4 are defective....Problem 4.29P:
There are two possible causes for a breakdown of a machine. To check the first possibility would...Problem 4.30P:
A person tosses a fair coin until a tail appears for the first time. If the tail appears on the nth...Problem 4.31P:
4.31. Each night different meteorologists give us the probability that it will rain the next day. To...Problem 4.32P:
To determine whether they have a certain disease, 100 people are to have their blood tested,...Problem 4.33P:
A newsboy purchases papers at 10 cents and sells them at 15 cents. However, he is not allowed to...Problem 4.35P:
A box contains 5 red and 5 blue marbles. Two marbles are withdrawn randomly. If they are the same...Problem 4.37P:
Consider Problem 4.22 t with i=2. Find the variance of the number of games played, and show that...Problem 4.38P:
Find Var (X) and Var (Y) for X and as given in Problem 4.21.Problem 4.39P:
If E[X]=1 and var(X)=5, find a. E[(2+X)2]; b. var(4+3X).Problem 4.40P:
A ball is drawn from an urn containing 3 white and 3 black balls. After the ball is drawn, it is...Problem 4.41P:
On a multiple-choice exam with 3 possible answers for each of the 5 questions, what is the...Problem 4.42P:
A man claims to have extrasensory perception. As a test, a fair coin is flipped 10 times and the man...Problem 4.43P:
A and B will take the same 10-question examination. Each question will be answered correctly by A...Problem 4.44P:
A communications channel transmits the digits 0 and 1. However, due to static, the digit transmitted...Problem 4.45P:
A satellite system consists of n components and functions on any given day if at least k of the n...Problem 4.46P:
A student is getting ready to take an important oral examination and is concerned about the...Problem 4.47P:
Suppose that it takes at least 9 votes from a 12-member jury to convict a defendant. Suppose also...Problem 4.48P:
In some military courts, 9 judges are appointed. However, both the prosecution and the defense...Problem 4.49P:
It is known that diskettes produced by a certain company will be defective with probability .01,...Problem 4.50P:
When coin 1 is flipped, it lands on heads with probability .4; when coin 2 is flipped, it lands on...Problem 4.51P:
Each member of a population of size n is, independently, female with probability p or male with...Problem 4.52P:
In a tournament involving players 1,2,3,4, players land 2 play a game, with the loser departing and...Problem 4.53P:
Suppose that a biased coin that lands on heads with probability p is flipped 10 times. Given that a...Problem 4.54P:
The expected number of typographical errors on a page of a certain magazine is .2. What is the...Problem 4.55P:
The monthly worldwide average number of airplane crashes of commercial airlines is 3.5. What is the...Problem 4.56P:
Approximately 80000 marriages took place in the state of New York last year. Estimate the...Problem 4.57P:
State your assumptions. Suppose that the average number of cars abandoned weekly on a certain...Problem 4.58P:
A certain typing agency employs 2 typists. The average number of errors per article is 3 when typed...Problem 4.59P:
How many people are needed so that the probability that at least one of them has the same birthday...Problem 4.60P:
Suppose that the number of accidents occurring on a highway each day is a Poisson random variable...Problem 4.61P:
Compare the Poisson approximation with the correct binomial probability for the following cases: a....Problem 4.62P:
If you buy a lottery ticket in 50 lotteries, in each of which your chance of winning a prize is...Problem 4.63P:
The number of times that a person contracts a cold in a given year is a Poisson random variable with...Problem 4.64P:
The probability of being dealt a full house in a hand of poker is approximately .0014. Find an...Problem 4.65P:
Consider n, independent trials, each of which results in one of the outcomes 1.. . ..k with...Problem 4.66P:
People enter a gambling casino at a rate of 1 every 2 minutes. a. What is the probability that no...Problem 4.67P:
The suicide rate in a certain state is 1 suicide per 100,000 inhabitants per month. a. Find the...Problem 4.68P:
Each of 500 soldiers in an army company independently has a certain disease with probability 1103....Problem 4.69P:
A total of 2n people, consisting of n married couples, are randomly seated (all possible orderings...Problem 4.71P:
In response to an attack of 10 missiles, 500 antiballistic missiles are launched. The missile...Problem 4.72P:
A fair coin is flipped 10 times. Find the probability that there is a string of 4 consecutive heads...Problem 4.73P:
At time 0, a coin that comes up heads with probability p is flipped and falls to the ground. Suppose...Problem 4.74P:
Consider a roulette wheel consisting of 38 numbers 1 through 36, 0, and double 0. If Smith always...Problem 4.75P:
Two athletic teams play a series of games; the first team to win 4 games is declared the overall...Problem 4.76P:
Suppose in Problem 4.75 that the two teams are evenly matched and each has probability 12 of winning...Problem 4.77P:
An interviewer is given a list of people she can interview. If the interviewer needs to interview 5...Problem 4.79P:
Solve the Banach match problem (Example 8e) when the left-hand matchbox originally contained N1...Problem 4.80P:
In the Banach matchbox problem, find the probability that at the moment when the first box is...Problem 4.81P:
An urn contains 4 white and 4 black balls. We randomly choose 4 balls, If 2 of them are white and 2...Problem 4.82P:
Suppose that a batch of 100 items contains 6 that are defective and 94 that are not defective. If X...Problem 4.83P:
A game popular in Nevada gambling casinos is Keno, which is played as follows: Twenty numbers are...Problem 4.84P:
In Example 81 what percentage of i defective lots does the purchaser reject? Find it for i = 1. 4....Problem 4.85P:
A purchaser of transistors buys them in lots of 20. It is his policy to randomly inspect 4...Problem 4.86P:
There are three highways in the county. The number of daily accidents that occur on these highways...Problem 4.87P:
Suppose that 10 balls are put into 5 boxes, with each ball independently being put in box i with...Problem 4.88P:
There are k types of coupons. Independently of the types of previously collected coupons, each new...Problem 4.89P:
An urn contains 10 red, S black, and 7 green balls. One of the colors is chosen at random (meaning...Problem 4.1TE:
There are N distinct types of coupons, and each time one is obtained it will, independently of past...Problem 4.3TE:
If X has distribution function F, what is the distribution function of the random variable x+, where...Problem 4.4TE:
The random variable X is said to have the Yule-Simons distribution if P{X=n}=4n(n+1)(n+2),n1 a. Show...Problem 4.5TE:
Let N be a nonnegative integer-valued random variable. For nonnegative values aj,j1, show that...Problem 4.7TE:
Let X be a random variable having expected value and variance 2. Find the expected value and...Problem 4.8TE:
Find Var (X) if P(X=a)=(1)=p=1P(X=b)Problem 4.9TE:
Show how the derivation of the binomial probabilities P{X=i}=(ni)pi(1p)ni,i=0,...,n leads to a proof...Problem 4.10TE:
Let X be a binomial random variable with parameters n and p. Show thatE[1X+1]=1(1p)n+1(n+1)pProblem 4.11TE:
Let X be the number of successes that result from 2n independent trials, when each trial is a...Problem 4.12TE:
Consider n independent sequential trials, each of which is successful with probability p. If there...Problem 4.13TE:
There are n components lined up in a linear arrangement. Suppose that each component independently...Problem 4.14TE:
Let X be a binomial random variable with parameters (n,p). What value of p maximizes...Problem 4.15TE:
A family has n children with probability pn,n1 where (1p)p. a. What proportion of families has no...Problem 4.16TE:
Suppose that n independent tosses of a coin having probability p of coming up heads are made. Show...Problem 4.17TE:
Let X be a Poisson random variable with parameter . Show that P{X=i} increases monotonically and...Problem 4.18TE:
Let X be a Poisson random variable with parameter a. Show that P{Xiseven}=12[1+e2] by using the...Problem 4.20TE:
Show that X is a Poisson random variable with parameter , then E[Xn]=E[(X+1)n1] Now use this result...Problem 4.21TE:
Consider n coins, each of which independently comes up heads with probability p. Suppose that n is...Problem 4.22TE:
From a set of n randomly chosen people, let Eij denote the event that persons i and j have the same...Problem 4.23TE:
An urn contains 2 n balls, of which 2 are numbered 1, 2 are numbered 2, .. ,, and 2 are numbered n....Problem 4.24TE:
Consider a random collection of n individuals. In approximating the probability that no 3 of these...Problem 4.25TE:
Here is another way to obtain a set of recursive equations for determining Pn, the probability that...Problem 4.26TE:
Suppose that the number of events that occur in a specifiedime is a Poisson random variable with...Problem 4.27TE:
Prove i=0nii!=1n!exxndx Hint: Use integration by parts.Problem 4.28TE:
If X is a geometric random variable, show analytically that P{X=n+kXn}=P{X=k}. Using the...Problem 4.29TE:
Let X be a negative binomial random variable with parameters n and p, and let Y be a binomial random...Problem 4.30TE:
For a hyper geometric random variable, determinePX=h+1)P{X=k}Problem 4.31TE:
Balls numbered I through N are in an urn. Suppose that n,nN, of them are randomly selected without...Problem 4.32TE:
A jar contains m+n chips, numbered 1, 2,. ., n+m. A set of size n, is drawn. If we let X denote the...Problem 4.36TE:
An urn initially contains one red and one blue ball. At each stage, a ball is randomly chosen and...Problem 4.3STPE:
A coin that when flipped comes up heads with probability p is flipped until either heads or tails...Problem 4.5STPE:
Suppose that P{X=0}=1P{X=1}. If E[X]=3Var(X), find P{X=0}.Problem 4.6STPE:
There are 2 coins in a bin. When one of them is flipped, it lands on heads with probability .6, and...Problem 4.10STPE:
An urn contains n balls numbered 1 through n. If you withdraw n balls randomly in sequence, each...Problem 4.13STPE:
Each of the members of a 7-judge panel independently makes a correct decision with probability .7....Problem 4.15STPE:
The number of eggs laid on a tree leaf by an insect of a certain type is a Poisson random variable...Problem 4.16STPE:
Each of n boys and n girls, independently and randomly, chooses a member of the other sex. If a boy...Problem 4.17STPE:
A total of 2n people, consisting of n married couples, are randomly divided into n pairs....Problem 4.20STPE:
Show that if X is a geometric random variable with parameter p, then E[1X]=plog(p)1p Hint: You will...Problem 4.21STPE:
Suppose that P{X=a}=p,P{X=b}=1p a. Show that Xbab is a Bernoulli random variable. b. Find Var(X).Problem 4.23STPE:
Balls are randomly withdrawn, one at a time without replacement, from an urn that initially has N...Problem 4.24STPE:
Ten balls are to be distributed among 5 urns, with each ball going into urn i with probability...Problem 4.25STPE:
For the match problem (Example 5m in Chapter 2), find a. the expected number of matches. b. the...Problem 4.26STPE:
Let be the probability that a geometric random variable X with parameter p is an even number. a....Problem 4.27STPE:
Two teams will play a series of games, with the winner being the first team to win a total of 4...Problem 4.28STPE:
An urn has n white and m black balls. Balls are randomly withdrawn, without replacement, until a...Problem 4.30STPE:
If X is a binomial random variable with parameters n and p, what type of random variable is nX.Browse All Chapters of This Textbook
Chapter 1 - Combinatorial AnalysisChapter 2 - Axioms Of ProbabilityChapter 3 - Conditional Probability And IndependenceChapter 4 - Random VariablesChapter 5 - Continuous Random VariablesChapter 6 - Jointly Distributed Random VariablesChapter 7 - Properties Of ExpectationChapter 8 - Limit TheoremsChapter 9 - Additional Topics In ProbabilityChapter 10 - Simulation
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EBK A FIRST COURSE IN PROBABILITY
9th Edition
ISBN: 9780321926678
A First Course In Probability
9th Edition
ISBN: 9789332519077
EBK A FIRST COURSE IN PROBABILITY
9th Edition
ISBN: 8220101467447
A First Course in Probability
9th Edition
ISBN: 9780321794772
A First Course In Probability
5th Edition
ISBN: 9780137463145
A First Course in Probability
8th Edition
ISBN: 9780136033134
A First Course In Probability, Global Edition
10th Edition
ISBN: 9781292269207
FIRST COURSE IN PROBABILITY (LOOSELEAF)
10th Edition
ISBN: 9780134753751
EBK FIRST COURSE IN PROBABILITY, A
10th Edition
ISBN: 9780134753676
EBK FIRST COURSE IN PROBABILITY, A
10th Edition
ISBN: 9780134753683
A Second Course in Probability
7th Edition
ISBN: 9780979570407
First Course In Probability, A (7th Edition)
7th Edition
ISBN: 9780131856622
A First Course In Probability (6th Edition)
6th Edition
ISBN: 9780130338518
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