 4.1P: Two balls are chosen randomly from an urn containing 8 white, 4 bla...
 4.1STE: Suppose that the random variable X is equal to the number of hits o...
 4.1TE: There are N distinct types of coupons, and each time one is obtaine...
 4.2P: Two fair dice are rolled. Let X equal the product of the 2 dice. Co...
 4.2STE: Suppose that X takes on one of the values 0, 1, and 2. If for some ...
 4.2TE: If X has distribution function F. what is the distribution function...
 4.3P: Three dice are rolled. By assuming that each of the 63 = 216 possib...
 4.3STE: A coin that when Hipped comes up heads with probability p is flippe...
 4.3TE: If X has distribution function F, what is the distribution function...
 4.4P: Five men and 5 women are ranked according to their scores on an exa...
 4.4STE: A certain community is composed of mfamilies, ni of which have i ch...
 4.4TE: The random variable X is said to have the YuleSimons distribution ...
 4.5P: Let X represent the difference between the number of heads and the ...
 4.5STE: Suppose that P{X = 0} = 1  P{X = 1}. If E[X]= 3Var(X), find P{X = 0}.
 4.6P: In Problem, for n = 3, if the coin is assumed fair, what are the pr...
 4.6STE: There are 2 coins in a bin. When one of them is flipped, it lands o...
 4.6TE: Let X be such thatP{X =1} = p = 1 – p{X = 1}Find c ? 1 such that E...
 4.7P: Suppose that a die is rolled twice. What are the possible values th...
 4.7STE: A philanthropist writes a positive number xona piece of red paper, ...
 4.7TE: Let X be a random variable having expected value ? and variance ?2....
 4.8P: If the die in assumed fair, calculate the probabilities associated ...
 4.8STE: Let B(n,p) represent a binomial random variable with parameters n a...
 4.8TE: Find Var(X) if
 4.9P: Repeat Example lc when the balls are selected with replacement.
 4.9STE: If X is a binomial random variable with expected value 6 and varian...
 4.9TE: Show how the derivation of the binomial probabilities leads to a pr...
 4.10P: Let X be the winnings of a gambler. Let p(i) = P(X = i) and suppose...
 4.10STE: An urn contains n balls numbered 1 through n. If you withdraw m bal...
 4.10TE: Let X be a binomial random variable with parameters n and p. Show that
 4.11P: (a) An integer N is to be selected at random from {1,2,..., (10)3} ...
 4.11STE: Teams A and B play a series of games, with the first team to win 3 ...
 4.11TE: Consider n independent sequential trials, each of which is successf...
 4.12P: In the game of TwoFinger Morra, 2 players show 1 or 2 fingers and ...
 4.12STE: A local soccer team has 5 more games left to play. If it wins its g...
 4.12TE: There are n components lined up in a linear arrangement. Suppose th...
 4.13P: A salesman has scheduled two appointments to sell encyclopedias. Hi...
 4.13STE: Each of the members of a 7judge panel independently makes a correc...
 4.13TE: Let X be a binomial random variable with parameters (n, p). What va...
 4.14P: A family has n children with probability ?pn,n ? 1, where ? ? (1 ? ...
 4.14STE: On average, 5.2 hurricanes hit a certain region in a year. What is ...
 4.14TE: A family has n children with probability ?pn,n ? 1, where ? ? (1 ? ...
 4.15P: The National Basketball Association (NBA) draft lottery involves th...
 4.15STE: The number of eggs laid on a tree leaf by an insect of a certain ty...
 4.15TE: Suppose that n independent tosses of a coin having probability p of...
 4.16P: In Problem, let team number 1 be the team with the worst record, le...
 4.16STE: Each of n boys and n girls, independently and randomly, chooses a m...
 4.16TE: Let X be a Poisson random variable with parameter X. Show that P{X ...
 4.17P: Suppose that the distribution function of X is given by (a) Find P{...
 4.17STE: A total of 2n people, consisting of n married couples, are randomly...
 4.17TE: Let X be a Poisson random variable with parameter ?.(a) Show that b...
 4.18P: Four independent flips of a fair coin are made. Let X denote the nu...
 4.18STE: A casino patron will continue to make $5 bets on red in roulette un...
 4.18TE: Let X be a Poisson random variable with parameter ?. What value of ...
 4.19P: If the distribution function of X is given by calculate the probabi...
 4.19STE: When three friends go for coffee, they decide who will pay the chec...
 4.19TE: Show that X is a Poisson random variable with parameter ?, then Now...
 4.20P: A gambling book recommends the following “winning strategy” for the...
 4.20STE: Show that if X is a geometric random variable with parameter p, then
 4.20TE: Consider n coins, each of which independently comes up heads with p...
 4.21P: Four buses carrying 148 students from the same school arrive at a f...
 4.21STE: Suppose that (a) Show that is a Bernoulli random variable._________...
 4.21TE: From a set of n randomly chosen people, let Eij denote the event th...
 4.22P: Suppose that two teams play a series of games that ends when one of...
 4.22STE: Each game you play is a win with probability p. You plan to play 5 ...
 4.23P: You have $1000, and a certain commodity presently sells for $2 per ...
 4.23STE: Balls are randomly withdrawn, one at a time without replacement, fr...
 4.24P: A and B play the following game: A writes down either number 1 or n...
 4.24STE: Ten balls are to be distributed among 5 urns, with each ball going ...
 4.25P: Two coins are to be flipped. The first coin will land on heads with...
 4.25STE: For the match problem (Example 5m in Chapter 2), find(a) the expect...
 4.25TE: Suppose that the number of events that occur in a specified time is...
 4.26P: One of the numbers 1 through 10 is randomly chosen. You are to try ...
 4.26STE: Let ? be the probability that a geometric random variable X with pa...
 4.26TE: Prove
 4.27P: An insurance company writes a policy to the effect that an amount o...
 4.27STE: The National Basketball Association championship series is a best o...
 4.27TE: If X is a geometric random variable, show analytically that Using t...
 4.28P: A sample of 3 items is selected at random from a box containing 20 ...
 4.28STE: An urn has n white and m black balls. Balls are randomly withdrawn,...
 4.28TE: Let X be a negative binomial random variable with parameters r and ...
 4.29P: There are two possible causes for a breakdown of a machine. To chec...
 4.29TE: For a hypergeometric random variable, determine
 4.30P: A person tosses a fair coin until a tail appears for the first time...
 4.30TE: Balls numbered 1 through N are in an urn. Suppose that n,n ? N, of ...
 4.31P: Each night different meteorologists give us the probability that it...
 4.31TE: A jar contains m + n chips, numbered 1,2,..., n + m. A set of size ...
 4.32P: To determine whether they have a certain disease, 100 people are to...
 4.32TE: A jar contains n chips. Suppose that a boy successively draws a chi...
 4.33P: A newsboy purchases papers at 10 cents and sells them at 15 cents. ...
 4.33TE: Repeat Theoretical Exercise, this time assuming that withdrawn chip...
 4.34P: In Example 4b, suppose that the department store incurs an addition...
 4.34TE: From a set of n elements, a nonempty subset is chosen at random in ...
 4.35P: A box contains 5 red and 5 blue marbles. Two marbles are withdrawn ...
 4.35TE: An urn initially contains one red and one blue ball. At each stage,...
 4.36P: Consider i  2. Find the variance of the number of games played, an...
 4.37P: Find Var(X) and Var(Y) for X and Y as given in 4.21. buses carrying...
 4.38P: If E[X] = 1 and Var(X) = 5, find(a) E[(2 + X)2]:(b) Var(4 + 3X).
 4.39P: A ball is drawn from an urn containing 3 white and 3 black balls. A...
 4.40P: On a multiplechoice exam with 3 possible answers for each of the 5...
 4.41P: A man claims to have extrasensory perception. As a test, a fair coi...
 4.42P: A and B will take the same 10question examination. Each question w...
 4.43P: A communications channel transmits the digits 0 and 1. However, due...
 4.44P: A satellite system consists of n components and functions on any gi...
 4.45P: A student is getting ready to take an important oral examination an...
 4.46P: Suppose that it takes at least 9 votes from a 12member jury to con...
 4.47P: In some military courts, 9 judges are appointed. However, both the ...
 4.48P: It is known that diskettes produced by a certain company will be de...
 4.49P: When coin 1 is llipped, it lands on heads with probability .4; when...
 4.50P: Suppose that a biased coin that lands on heads with probability p i...
 4.51P: The expected number of typographical errors on a page of a certain ...
 4.52P: The monthly worldwide average number of airplane crashes of commerc...
 4.53P: Approximately 80,000 marriages took place in the state of New York ...
 4.54P: Suppose that the average number of cars abandoned weekly on a certa...
 4.55P: A certain typing agency employs 2 typists. The average number of er...
 4.56P: How many people are needed so that the probability that at least on...
 4.57P: Suppose that the number of accidents occurring on a highway each da...
 4.58P: Compare the Poisson approximation with the correct binomial probabi...
 4.59P: If you buy a lottery ticket in 50 lotteries, in each of which your ...
 4.60P: The number of times that a person contracts a cold in a given year ...
 4.61P: The probability of being dealt a full house in a hand of poker is a...
 4.62P: Consider n independent trials, each of which results in one of the ...
 4.63P: People enter a gambling casino at a rate of 1 every 2 minutes.(a) W...
 4.64P: The suicide rate in a certain state is 1 suicide per 100,000 inhabi...
 4.65P: Each of 500 soldiers in an army company independently has a certain...
 4.66P: A total of 2n people, consisting of n married couples, are randomly...
 4.68P: In response to an attack of 10 missiles, 500 antiballistic missiles...
 4.69P: A fair coin is flipped 10 times. Find the probability that there is...
 4.70P: At time 0, a coin that comes up heads with probability p is flipped...
 4.71P: Consider a roulette wheel consisting of 38 numbers 1 through 36, 0,...
 4.72P: Two athletic teams play a scries of games; the first team to win 4 ...
 4.73P: Suppose in 4.72 that the two teams are evenly matched and each has ...
 4.74P: An interviewer is given a list of people she can interview. If the ...
 4.75P: A fair coin is continually flipped until heads appears for the 10th...
 4.76P: Solve the Banach match problem (Example 8e) when the lefthand matc...
 4.77P: In the Banach matchbox problem, find the probability that at the mo...
 4.78P: An urn contains 4 white and 4 black balls. We randomly choose 4 bal...
 4.79P: Suppose that a batch of 100 items contains 6 that are defective and...
 4.80P: A game popular in Nevada gambling casinos is Keno, which is played ...
 4.81P: In Example 8i, what percentage of i defective lots does the purchas...
 4.82P: A purchaser of transistors buys them in lots of 20. It is his polic...
 4.83P: There are three highways in the county. The number of daily acciden...
 4.84P: Suppose that 10 balls are put into 5 boxes, with each ball independ...
Solutions for Chapter 4: A First Course in Probability 9th Edition
Full solutions for A First Course in Probability  9th Edition
ISBN: 9780321794772
Solutions for Chapter 4
Get Full SolutionsChapter 4 includes 142 full stepbystep solutions. A First Course in Probability was written by and is associated to the ISBN: 9780321794772. Since 142 problems in chapter 4 have been answered, more than 62401 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: A First Course in Probability , edition: 9. This expansive textbook survival guide covers the following chapters and their solutions.

Alias
In a fractional factorial experiment when certain factor effects cannot be estimated uniquely, they are said to be aliased.

All possible (subsets) regressions
A method of variable selection in regression that examines all possible subsets of the candidate regressor variables. Eficient computer algorithms have been developed for implementing all possible regressions

Analysis of variance (ANOVA)
A method of decomposing the total variability in a set of observations, as measured by the sum of the squares of these observations from their average, into component sums of squares that are associated with speciic deined sources of variation

Asymptotic relative eficiency (ARE)
Used to compare hypothesis tests. The ARE of one test relative to another is the limiting ratio of the sample sizes necessary to obtain identical error probabilities for the two procedures.

Biased estimator
Unbiased estimator.

Conditional probability density function
The probability density function of the conditional probability distribution of a continuous random variable.

Conidence interval
If it is possible to write a probability statement of the form PL U ( ) ? ? ? ? = ?1 where L and U are functions of only the sample data and ? is a parameter, then the interval between L and U is called a conidence interval (or a 100 1( )% ? ? conidence interval). The interpretation is that a statement that the parameter ? lies in this interval will be true 100 1( )% ? ? of the times that such a statement is made

Contrast
A linear function of treatment means with coeficients that total zero. A contrast is a summary of treatment means that is of interest in an experiment.

Cook’s distance
In regression, Cook’s distance is a measure of the inluence of each individual observation on the estimates of the regression model parameters. It expresses the distance that the vector of model parameter estimates with the ith observation removed lies from the vector of model parameter estimates based on all observations. Large values of Cook’s distance indicate that the observation is inluential.

Covariance
A measure of association between two random variables obtained as the expected value of the product of the two random variables around their means; that is, Cov(X Y, ) [( )( )] =? ? E X Y ? ? X Y .

Defect concentration diagram
A quality tool that graphically shows the location of defects on a part or in a process.

Deining relation
A subset of effects in a fractional factorial design that deine the aliases in the design.

Dependent variable
The response variable in regression or a designed experiment.

Design matrix
A matrix that provides the tests that are to be conducted in an experiment.

Distribution function
Another name for a cumulative distribution function.

Erlang random variable
A continuous random variable that is the sum of a ixed number of independent, exponential random variables.

Error sum of squares
In analysis of variance, this is the portion of total variability that is due to the random component in the data. It is usually based on replication of observations at certain treatment combinations in the experiment. It is sometimes called the residual sum of squares, although this is really a better term to use only when the sum of squares is based on the remnants of a modelitting process and not on replication.

Estimate (or point estimate)
The numerical value of a point estimator.

Estimator (or point estimator)
A procedure for producing an estimate of a parameter of interest. An estimator is usually a function of only sample data values, and when these data values are available, it results in an estimate of the parameter of interest.

Finite population correction factor
A term in the formula for the variance of a hypergeometric random variable.