Explanation Given: In a contest originating with n players each player independently advances to the next round with player i advancing with probability p i . Calculation: Note that X i ≥ k will occur if advances at least k times and at least one of the other players advances at least k − 1 times. The probability that the player j does not advance k is 1 − p j k . So, the probability that none of the players except i advances k times is ∏ j ≠ i ( 1 − p j k ) To determine To find P ( i is either the sole or the co-winner). To determine To find P ( i is the sole winner).

A First Course In Probability, Global Edition

10th Edition

ISBN: 9781292269207

Author: Ross, Sheldon

Publisher: PEARSON

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Chapter 6, Problem 6.25STPE

To determine

To find P(Xi≥k)

To determine

To find P(i is either the sole or the co-winner).

To determine

To find P(i is the sole winner).

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Chapter 6, Problem 6.24STPE

Chapter 6, Problem 6.26STPE

Chapter 6 Solutions

A First Course In Probability, Global Edition

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. 6.8P Ch. 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. 6.17P Ch. 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. 6.20P Ch. 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. 6.23P Ch. 6 - Consider independent trials, each of which results...Ch. 6 - Suppose that 106 people arrive at a service...Ch. 6 - Prob. 6.26P Ch. 6 - Prob. 6.27P Ch. 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 - Let X1 and X2 be independent normal random...Ch. 6 - Prob. 6.34P Ch. 6 - Teams 1, 2, 3, 4 are all scheduled to play each of...Ch. 6 - Let X1,...,X10 be independent with the same...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. 6.41P Ch. 6 - Prob. 6.42P Ch. 6 - Prob. 6.43P Ch. 6 - The joint probability mass function of X and Y is...Ch. 6 - Prob. 6.45P Ch. 6 - Prob. 6.46P Ch. 6 - An insurance company supposes that each person has...Ch. 6 - If X1,X2,X3 are independent random variables that...Ch. 6 - Prob. 6.49P Ch. 6 - If 3 trucks break down at points randomly...Ch. 6 - Consider a sample of size 5 from a uniform...Ch. 6 - Prob. 6.52P Ch. 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. 6.57P Ch. 6 - Prob. 6.58P Ch. 6 - Prob. 6.59P Ch. 6 - Prob. 6.60P Ch. 6 - Repeat Problem 6.60 when X and Y are independent...Ch. 6 - Prob. 6.62P Ch. 6 - Prob. 6.63P Ch. 6 - In Example 8b, let Yk+1=n+1i=1kYi. Show that...Ch. 6 - Consider an urn containing n balls numbered 1.. .....Ch. 6 - Suppose X,Y have a joint distribution function...Ch. 6 - Prob. 6.2TE Ch. 6 - Prob. 6.3TE Ch. 6 - Solve Buffons needle problem when LD.Ch. 6 - If X and Y are independent continuous positive...Ch. 6 - Prob. 6.6TE Ch. 6 - Prob. 6.7TE Ch. 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. 6.11TE Ch. 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. 6.18TE Ch. 6 - Let X1,X2,X3 be independent and identically...Ch. 6 - Prob. 6.20TE Ch. 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 - Suppose that X1,...,Xn are independent exponential...Ch. 6 - Establish Equation (6.2) by differentiating...Ch. 6 - Show that the median of a sample of size 2n+1 from...Ch. 6 - Prob. 6.30TE 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. 6.35TE Ch. 6 - Prob. 6.36TE Ch. 6 - Suppose that (X,Y) has a bivariate normal...Ch. 6 - Suppose that X has a beta distribution with...Ch. 6 - 6.39. Consider an experiment with n possible...Ch. 6 - Prob. 6.40TE Ch. 6 - Prob. 6.41TE Ch. 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. 6.3STPE Ch. 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. 6.11STPE Ch. 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. 6.15STPE Ch. 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...Ch. 6 - In Example 1c, find P(Xr=i,Ys=j) when ji.Ch. 6 - A Pareto random variable X with parameters a0,0...Ch. 6 - Prob. 6.24STPE Ch. 6 - Prob. 6.25STPE Ch. 6 - Let X1,...,Xn, be independent nonnegative integer...

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To find P ( X i ≥ k )

Solution Summary: The author calculates that in a contest originating with n players each player independently advances to the next round.

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To find P(Xi≥k)

To find P(i is either the sole or the co-winner).

To find P(i is the sole winner).

Want to see the full answer?

Chapter 6 Solutions