A First Course in Probability
9th Edition
ISBN: 9780321794772
Author: Sheldon Ross
Publisher: PEARSON
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Chapter 6, Problem 6.7P
Consider a sequence of independent Bernoulli trials, each of which is a success with
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Chapter 6 Solutions
A First Course in Probability
Ch. 6 - Two fair dice are rolled. Find the joint...Ch. 6 - Suppose that 3 balls are chosen without...Ch. 6 - In Problem 8 t, suppose that the white balls are...Ch. 6 - Repeat Problem 6.2 when the ball selected is...Ch. 6 - Repeat Problem 6.3a when the ball selected is...Ch. 6 - The severity of a certain cancer is designated by...Ch. 6 - Consider a sequence of independent Bernoulli...Ch. 6 - Prob. 6.8PCh. 6 - The joint probability density function of X and Y...Ch. 6 - Prob. 6.10P
Ch. 6 - In Example Id, verify that f(x,y)=2exe2y,0x,0y, is...Ch. 6 - The number of people who enter a drugstore in a...Ch. 6 - A man and a woman agree to meet at a certain...Ch. 6 - An ambulance travels back and forth at a constant...Ch. 6 - The random vector (X,Y) is said to be uniformly...Ch. 6 - Suppose that n points are independently chosen at...Ch. 6 - Prob. 6.17PCh. 6 - Let X1 and X2 be independent binomial random...Ch. 6 - Show that f(x,y)=1x, 0yx1 is a joint density...Ch. 6 - Prob. 6.20PCh. 6 - Let f(x,y)=24xy0x1,0y1,0x+y1 and let it equal 0...Ch. 6 - The joint density function of X and Y is...Ch. 6 - Prob. 6.23PCh. 6 - Consider independent trials, each of which results...Ch. 6 - Suppose that 106 people arrive at a service...Ch. 6 - Prob. 6.26PCh. 6 - Prob. 6.27PCh. 6 - The time that it takes to service a car is an...Ch. 6 - The gross daily sales at a certain restaurant are...Ch. 6 - Jills bowling scores are approximately normally...Ch. 6 - According to the U.S. National Center for Health...Ch. 6 - Monthly sales are independent normal random...Ch. 6 - The expected number of typographical errors on a...Ch. 6 - The monthly worldwide average number of airplane...Ch. 6 - In Problem 6.4, calculate the conditional...Ch. 6 - In Problem 6.3 calculate the conditional...Ch. 6 - Prob. 6.37PCh. 6 - Prob. 6.38PCh. 6 - Prob. 6.39PCh. 6 - The joint probability mass function of X and Y is...Ch. 6 - Prob. 6.41PCh. 6 - Prob. 6.42PCh. 6 - An insurance company supposes that each person has...Ch. 6 - If X1,X2,X3 are independent random variables that...Ch. 6 - Prob. 6.45PCh. 6 - If 3 trucks break down at points randomly...Ch. 6 - Consider a sample of size 5 from a uniform...Ch. 6 - Prob. 6.48PCh. 6 - Let X(1),X(2),...,X(n) be the order statistics of...Ch. 6 - Let Z1 and Z2 be independent standard normal...Ch. 6 - Derive the distribution of the range of a sample...Ch. 6 - Let X and Y denote the coordinates of a point...Ch. 6 - Prob. 6.53PCh. 6 - Prob. 6.54PCh. 6 - Prob. 6.55PCh. 6 - Prob. 6.56PCh. 6 - Repeat Problem 6.60 when X and Y are independent...Ch. 6 - Prob. 6.58PCh. 6 - Prob. 6.59PCh. 6 - In Example 8b, let Yk+1=n+1i=1kYi. Show that...Ch. 6 - Consider an urn containing n balls numbered 1.. .....Ch. 6 - Verify equation (1.2).Ch. 6 - Suppose that the number of events occurring in a...Ch. 6 - Prob. 6.3TECh. 6 - Solve Buffons needle problem when LD.Ch. 6 - If X and Y are independent continuous positive...Ch. 6 - Prob. 6.6TECh. 6 - Prob. 6.7TECh. 6 - Let X and Y be independent continuous random...Ch. 6 - Let X1,...,Xn be independent exponential random...Ch. 6 - The lifetimes of batteries are independent...Ch. 6 - Prob. 6.11TECh. 6 - Show that the jointly continuous (discrete) random...Ch. 6 - In Example 5e t, we computed the conditional...Ch. 6 - Suppose that X and Y are independent geometric...Ch. 6 - Consider a sequence of independent trials, with...Ch. 6 - If X and Y are independent binomial random...Ch. 6 - Suppose that Xi,i=1,2,3 are independent Poisson...Ch. 6 - Prob. 6.18TECh. 6 - Let X1,X2,X3 be independent and identically...Ch. 6 - Prob. 6.20TECh. 6 - Suppose that W, the amount of moisture in the air...Ch. 6 - Let W be a gamma random variable with parameters...Ch. 6 - A rectangular array of mn numbers arranged in n...Ch. 6 - If X is exponential with rate , find...Ch. 6 - Suppose thatF(x) is a cumulative distribution...Ch. 6 - Show that if n people are distributed at random...Ch. 6 - Establish Equation (6.2) by differentiating...Ch. 6 - Show that the median of a sample of size 2n+1 from...Ch. 6 - Verify equation (6.6), which gives the joint...Ch. 6 - Compute the density of the range of a sample of...Ch. 6 - Let X(1)X(2)...X(n) be the ordered values of n...Ch. 6 - Let X1,...,Xn be a set of independent and...Ch. 6 - Let X1,....Xn, be independent and identically...Ch. 6 - Prob. 6.34TECh. 6 - Prob. 6.35TECh. 6 - Each throw of an unfair die lands on each of the...Ch. 6 - The joint probability mass function of the random...Ch. 6 - Prob. 6.3STPECh. 6 - Let r=r1+...+rk, where all ri are positive...Ch. 6 - Suppose that X, Y, and Z are independent random...Ch. 6 - Let X and Y be continuous random variables with...Ch. 6 - The joint density function of X and Y...Ch. 6 - Consider two components and three types of shocks....Ch. 6 - Consider a directory of classified advertisements...Ch. 6 - The random parts of the algorithm in Self-Test...Ch. 6 - Prob. 6.11STPECh. 6 - The accompanying dartboard is a square whose sides...Ch. 6 - A model proposed for NBA basketball supposes that...Ch. 6 - Let N be a geometric random variable with...Ch. 6 - Prob. 6.15STPECh. 6 - You and three other people are to place bids for...Ch. 6 - Find the probability that X1,X2,...,Xn is a...Ch. 6 - 6.18. Let 4VH and Y, be independent random...Ch. 6 - Let Z1,Z2.....Zn be independent standard normal...Ch. 6 - Let X1,X2,... be a sequence of independent and...Ch. 6 - Prove the identity P{Xs,Yt}=P{Xs}+P{Yt}+P{Xs,Yt}1...
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- A local zoo imported seven rare birds from a South American country. Suppose that among the seven, three have a fatal disease. As usual, a customs officer must inspect and so he randomnly selects three birds and sends them for testing. If we let X denote the number of diseased birds, it can be shown that the probability mass function of X is: if r = 0, 1, 2, 3, px (r) = () 0. otherwise. What is P(1 < X < 2)? O 0.3429 O 0.5143 O 0.6531 O 0.7716 O 0.8571arrow_forwardQ5. A box of 10 transistors is known to contain 2 that are defective. The transistors are to be tested, one at a time, until the defective ones are identified. Denote N₁ the number of tests made until the first defective is spotted and by N₂ the number of additional tests until the second defective is spotted. Find the joint probability mass function p(3, 3).arrow_forwardTwo balls are chosen randomly from an urn containing 8 white, 4 black, and 2 orange balls. Suppose that we win $2 for each black ball selected and we lose $1 for each white ball selected. Let X denote our winnings. Find the probability mass function of X.arrow_forward
- Two friends play a ball picking game where one wants to avoid the ‘black’ ball: The two friends each have a bag with 2 balls (1 black and 1 red) and they each randomly choose one ball out of their bag. Whoever picks a black ball must pay the other person $1 no matter what the other friend selected. If both friends choose the red ball, nobody wins or loses any money. Say you played this game with you friend. Find the probability mass function (pmf) for your net winnings (in $) from this game. Display it in table form.arrow_forwardAn urn contains 4 red balls and 3 green balls. Two balls are drawn randomly. (a) Let Z denote the number of green balls in the sample when the draws are done without replacement. Give the possible values and the probability mass function of Z. (b) Let W denote the number of green balls in the sample when the draws are done with replacement. Give the possible values and the probability mass function of W.arrow_forwardIn a batch of 23 pedometers, 3 are believed to be defective. A quality-control engineer randomly selects 7 units to test. Let random variable X the number of defective units that are among the 7 units tested. a. Find the probability mass function f(x)=P(X=x), and sketch its histogram b. Find P(X=1). What does this number represent? c. Find P(X2 1). What does this number represent? Using the hypergeometric probability distribution model, set up an expression that can be used to find a single ordered pair in the probability mass function (x)-P(X) (912) 10x)-POX-x)+ 00 28287261 (Simply your answers) Find the probabiety mass function (x) POC) -O (Type an ordered pair Use a comma to separate answers as needed Round to five deamal places a needed) Let the number of defective pedometers among 7 uns tested, and lyfo Choose the comect stagram OA Oc Cocon PARADA LEADERSarrow_forward
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