A First Course In Probability, Global E...10th EditionRoss, Sheldon Publisher: PEARSONISBN: 9781292269207
A First Course In Probability, Global E...
Solutions for A First Course In Probability, Global Edition
Problem 7.1P:
A player throws a fair die and simultaneously flips a fair coin, If the coin lands heads, then she...Problem 7.2P:
The game of Clue involves 6 suspects, 6 weapons, and 9 rooms. One of each is randomly chosen and the...Problem 7.3P:
Gambles are independent, and each one results in the player being equally likely to win or lose 1...Problem 7.5P:
The county hospital is located at the center of a square whose sides are 3 miles wide. If an...Problem 7.7P:
Suppose that A and B each randomly and independently choose 3 of 10 objects. Find the expected...Problem 7.8P:
N people arrive separately to a professional dinner. Upon arrival, each person looks to see if he or...Problem 7.9P:
A total of n. balls, numbered 1 through n, are put into n urns, also numbered 1 through n in such a...Problem 7.10P:
Consider 3 trials, each having the same probability of success. Let X denote the total number of...Problem 7.11P:
Consider n independent flips of a coin having probability p of landing on heads. Say that a...Problem 7.12P:
A group of n men and n women is lined up at random. a. Find the expected number of men who have a...Problem 7.13P:
A set of 1000 cards numbered 1 through 1000 is randomly distributed among 1000 people with each...Problem 7.14P:
An urn has m black balls. At each stage, a black ball is removed and a new ball that is black with...Problem 7.15P:
In Example 2h, say that i and j, ij form a matched pair if i chooses the hat belonging to j and j...Problem 7.16P:
Let Z be a standard normal random variable, and, for a fixed x. set X={XifXx0otherwise Show that...Problem 7.17P:
A deck of n cards numbered 1 through n is thoroughly shuffled so that all possible n! orderings can...Problem 7.18P:
Cards from an ordinary deck of 52 playing cards are turned face up one at a time. If the 1st card is...Problem 7.21P:
For a group of 100 people, compute a. the expected number of days of the year that are birthdays of...Problem 7.22P:
How many times would you expect to roll a fair die before all 6 sides appeared at least once?Problem 7.23P:
Urn I contains 5 white and 6 black balls, while urn 2 contains 8 white and 10 black balls. Two balls...Problem 7.24P:
A bottle initially contains m large pills and n small pills. Each day, a patient randomly chooses...Problem 7.25P:
Let X1,X2... be a sequence of independent and identically distributed continuous random variables....Problem 7.26P:
If X1,X2,....Xn are independent and identically distributed random variables having uniform...Problem 7.27P:
If 101 items are distributed among 10 boxes, then at least one of the boxes must contain more than...Problem 7.29P:
There are 4 different types of coupons, the first 2 of which comprise one group and the second 2...Problem 7.30P:
If X and Y are independent and identically distributed with mean and variance2 find E[(XY)2]Problem 7.33P:
If E[X]=1 and Var(X)=5, find a. E[(2+X)2]: b. Var(4+3X).Problem 7.34P:
If 10 married couples are randomly seated at a round table, compute (a) the expected number and (b)...Problem 7.35P:
Cards from an ordinary deck are turned face up one at a time. Compute the expected number of cards...Problem 7.36P:
Let X be the number of ls and F the number of 2s that occur in n rolls of a fair die. Compute...Problem 7.37P:
A die is rolled twice. Let X equal the sum of the outcomes, and let Y equal the first outcome minus...Problem 7.38P:
Suppose X and Y have the following joint probability mass...Problem 7.39P:
Suppose that 2 balls are randomly removed from an urn containing n red and m blue balls. Let Xi=1 if...Problem 7.41P:
Let X1,... be independent with common mean and common variance 2 and setYn=Xn+Xn+1+Xn+2. For j0....Problem 7.43P:
A pond contains 100 fish, of which 30 are carp. If 20 fish are caught, what are the mean and...Problem 7.44P:
A group of 20 people consisting of 10 men and 10 women is randomly arranged into 10 pairs of 2 each....Problem 7.45P:
Let X1,X2,...,Xn be independent random variables having an unknown continuous distribution function...Problem 7.46P:
Between two distinct methods for manufacturing certain goods, the quality of goods produced by...Problem 7.48P:
Consider the following dice game. as played at a certain gambling casino: Players 1 and 2 roll a...Problem 7.50P:
A fair die is successively rolled. Let X and Y denote, respectively, the number of rolls necessary...Problem 7.51P:
There are two misshapen coins in a box; their probabilities for landing on heads when they are...Problem 7.54P:
A population is made up of r disjoint subgroups. Let pi denote the proportion of the population that...Problem 7.55P:
A prisoner is trapped in a cell containing 3 doors. The first door leads to a tunnel that returns...Problem 7.56P:
Consider the following dice game: A pair of dice is rolled. If the sum is 7, then the game ends and...Problem 7.57P:
Ten hunters are waiting for ducks to fly by. When a flock of ducks flies overhead, the hunters fire...Problem 7.58P:
The number of people who enter an elevator on the ground floor is a Poisson random variable with...Problem 7.59P:
Suppose that the expected number of accidents per week at an industrial plant is 5. Suppose also...Problem 7.60P:
A coin having probability p of coming up heads is continually flipped until both heads and tails...Problem 7.61P:
A coin that comes up heads with probability p is continually flipped. Let N be the number of flips...Problem 7.62P:
There are n+1 participants in a game. Each person independently is a winner with probability p. The...Problem 7.63P:
Each of m+2 players pays 1 unit to a kitty in order to play the following game: A fair coin is to be...Problem 7.64P:
The number of goals that J scores in soccer games that her team wins is Poisson distributed with...Problem 7.69P:
Type i light bulbs function for a random amount of time having mean i, and standard deviation...Problem 7.70P:
The number of winter storms in a good year is a Poisson random variable with mean 3, whereas the...Problem 7.71P:
In Example 5c, compute the variance of the length of time until the miner reaches safety.Problem 7.73P:
The number of accidents that a person has in a given year is a Poisson random variable with mean ....Problem 7.74P:
Repeat Problem 7.73 when the proportion of the population having a value of less than x is equal to...Problem 7.75P:
Consider an urn containing a large number of coins, and suppose that each of the coins has some...Problem 7.76P:
In problem ,suppose that the coin is tossed n times. Let X denote the number of heads that occur....Problem 7.77P:
Suppose that in Problem 7.75, we continue to flip the coin until a head appears. Let N denote the...Problem 7.78P:
In Example 6b, let S denote the signal sent and R the signal received. a. Compute E[R]. b. Compute...Problem 7.79P:
In Example 6c y)2].Problem 7.80P:
The moment generating function of X is given by MX(t)=exp{2et2} and that of Y by MY(t)=(34et+14)10....Problem 7.81P:
Let X be the value of the first die and Y the sum of the values when two dice are rolled. Compute...Problem 7.82P:
The joint density of X and Y is given by f(x,y)=12eye(xy)220y,x a. Compute the joint moment...Problem 7.84P:
Successive weekly sales, in units of $1,000, have a bivariate normal distribution with common mean...Problem 7.1TE:
Show that E[(Xa)2] is minimized at a=E[X].Problem 7.2TE:
Suppose that X is a continuous random variable with density function f. Show that E[|Xa|] is...Problem 7.4TE:
Let X be a random variable having finite expectation and variance 2 and let g(•) be a twice...Problem 7.8TE:
We say that X is stochastically larger than Y, written XstY, if, for all t, P{Xt}P{Yt} Show that if...Problem 7.10TE:
A coin having probability p of landing on heads is flipped n times. Compute the expected number of...Problem 7.11TE:
Let X1,X2,....Xn be independent and identically distributed positive random variables. For kn, find...Problem 7.13TE:
Let X1,X2,... be a sequence of independent random variables having the probability mass function...Problem 7.19TE:
In Example 41 t, we showed that the covariance of the multinomial random variables Ni and Nj is...Problem 7.20TE:
Show that X and Y are identically distributed and not necessarily independent, then cov(X+Y,XY)=0Problem 7.24TE:
Show that Z is a standard normal random variable and if Y is defined by Y=a+bZ+eZ2, then...Problem 7.25TE:
Prove the Cauchy-Schwarz inequality, namely, (E[XY])2E[X2]E[Y2] Hint: Unless Y=tX for some constant,...Problem 7.26TE:
Show that if X and Y are independent, then E[XY=y]=E[X] for all y a. in the discrete case; b. in the...Problem 7.27TE:
Prove that E[g(X)YX]=g(X)E[YX].Problem 7.28TE:
Prove that if E[YX=x]=E[Y] for all x, then X and Y are uncorrelated; give a counterexample to show...Problem 7.30TE:
Let X1,...,Xn be independent and identically distributed random variables, FindE[X1X1+...+Xn=x]Problem 7.31TE:
Consider Example 4f, which is concerned with the multinomial distribution. Use conditional...Problem 7.32TE:
An urn initially contains b black and w white balls. At each stage, we add r black balls and then...Problem 7.33TE:
For an event A, let IA equal 1 if A occurs and let it equal 0 if A does not occur. For a random...Problem 7.34TE:
A coin that lands on heads with probability p is continually flipped. Compute the expected number of...Problem 7.35TE:
For another approach to Theoretical Exercise 7.34, let Tr denote the number of flips required to...Problem 7.36TE:
The probability generating function of the discrete nonnegative integer valued random variable X...Problem 7.37TE:
One ball at a time is randomly selected from an urn containing a white and b black balls until all...Problem 7.40TE:
The best quadratic predictor of Y with respect to X is a+bX+cX2, where a, b, and c are chosen to...Problem 7.41TE:
Use the conditional variance formula to determine the variance of a geometric random variable X...Problem 7.42TE:
Let X be a normal random variable with parameters =0 and 2=1, and let I, independent of X, be such...Problem 7.43TE:
It follows from Proposition 6.1 and the fact that the best linear predictor of Y with respect to...Problem 7.46TE:
Verify the formula for the moment generating function of a uniform random variable that is given in...Problem 7.47TE:
For a standard normal random variable Z, let n=E[Zn]. Show thatn={0whennisodd(2j)!2jj!whenn=2j Hint:...Problem 7.50TE:
The positive random variable X is said to be a lognormal random variable with parameters and 2 if...Problem 7.51TE:
Let X have moment generating function M(t), and define (t)=logM(t). Show that (t)t=0=var(X)Problem 7.52TE:
Use Table 7.2 to determine the distribution of i=1nXi when X1,...,Xn are independent and identically...Problem 7.54TE:
Suppose that X1,...,Xn have a multivariate normal distribution. Show that X1,...,Xn are independent...Problem 7.55TE:
If Z is a standard normal random variable, what is cov(Z,Z2)?Problem 7.56TE:
Suppose that Y is a normal random variable with mean and variance 2, and suppose also that the...Problem 7.1STPE:
Consider a list of m names, where the same name may appear more than once on the list. Let...Problem 7.19STPE:
There are n items in a box labeled H and m in a box labeled T. A coin that comes up heads with...Problem 7.20STPE:
Let X be a nonnegative random variable having distribution function F. Show that if F(x)=1F(x) ,then...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
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A First Course In Probability
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EBK FIRST COURSE IN PROBABILITY, A
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