FIRST COURSE IN PROBABILITY (LOOSELEAF)10th EditionRoss Publisher: PEARSONISBN: 9780134753751
FIRST COURSE IN PROBABILITY (LOOSELEAF)
Solutions for FIRST COURSE IN PROBABILITY (LOOSELEAF)
Problem 6.1P:
Two fair dice are rolled. Find the joint probability mass function of X and Y when a. X is the...Problem 6.2P:
Suppose that 3 balls are chosen without replacement from an urn consisting of 5 white and 8 red...Problem 6.3P:
In Problem 8 t, suppose that the white balls are numbered, and let Yi equal 1 if the ith white ball...Problem 6.4P:
Repeat Problem 6.2 when the ball selected is replaced in the urn before the next selection.Problem 6.5P:
Repeat Problem 6.3a when the ball selected is replaced in the urn before the next selection.Problem 6.6P:
The severity of a certain cancer is designated by one of the grades 1,2,3,4 with 1 being the least...Problem 6.7P:
Consider a sequence of independent Bernoulli trials, each of which is a success with probability p....Problem 6.9P:
The joint probability density function of X and Y is given by f(x,y)=67(x2+xy2)0x1,0y2 a. Verify...Problem 6.11P:
In Example Id, verify that f(x,y)=2exe2y,0x,0y, is indeed a joint density, function. That is, check...Problem 6.12P:
The number of people who enter a drugstore in a given hour is a Poisson random variable with...Problem 6.13P:
A man and a woman agree to meet at a certain location about 12:30 P.M. If the man arrives at a time...Problem 6.14P:
An ambulance travels back and forth at a constant speed along a road of length L. At a certain...Problem 6.15P:
The random vector (X,Y) is said to be uniformly distributed over a region R in the plane if, for...Problem 6.16P:
Suppose that n points are independently chosen at random on the circumference of a circle, and we...Problem 6.18P:
Let X1 and X2 be independent binomial random variables with Xi having parameters (ni,pi),i=1,2. Find...Problem 6.19P:
Show that f(x,y)=1x, 0yx1 is a joint density function. Assuming that f is the joint density function...Problem 6.21P:
Let f(x,y)=24xy0x1,0y1,0x+y1 and let it equal 0 otherwise. a. Show that f(xy) is a joint probability...Problem 6.22P:
The joint density function of X and Y is f(x,y)={x+y0x1,0y10otherwise a. Are X and Y independent? b....Problem 6.24P:
Consider independent trials, each of which results in outcome i,i=0,1,...,k with probability...Problem 6.25P:
Suppose that 106 people arrive at a service station at times that are independent random variables,...Problem 6.28P:
The time that it takes to service a car is an exponential random variable with rate 1. a. If A. J....Problem 6.29P:
The gross daily sales at a certain restaurant are a normal random variable with mean $2200 and...Problem 6.30P:
Jills bowling scores are approximately normally distributed with mean 170 and standard deviation 20,...Problem 6.31P:
According to the U.S. National Center for Health Statistics, 25.2 percent of males and 23.6 percent...Problem 6.32P:
Monthly sales are independent normal random variables with mean 100 and standard deviation a. Find...Problem 6.33P:
Let X1 and X2 be independent normal random variables, each having mean 10 and variance 2. Which...Problem 6.35P:
Teams 1, 2, 3, 4 are all scheduled to play each of the other teams 10 times. Whenever team i plays...Problem 6.36P:
Let X1,...,X10 be independent with the same continuous distribution function F and let m be the...Problem 6.37P:
The expected number of typographical errors on a page of a certain magazine is .2. What is the...Problem 6.38P:
The monthly worldwide average number of airplane crashes of commercial airlines is 2.2. What is the...Problem 6.39P:
In Problem 6.4, calculate the conditional probability mass function of X1 given that a. X2=1; b....Problem 6.40P:
In Problem 6.3 calculate the conditional probability mass function of Y1 given that a. Y2=1; b....Problem 6.44P:
The joint probability mass function of X and Y is given byP(1,1)=18p(1,2)=14P(2,1)=18p(2,2)=12 a....Problem 6.47P:
An insurance company supposes that each person has an accident parameter and that the yearly number...Problem 6.48P:
If X1,X2,X3 are independent random variables that are uniformly distributed over (0, 1), compute the...Problem 6.50P:
If 3 trucks break down at points randomly distributed on a road of length L find the probability...Problem 6.51P:
Consider a sample of size 5 from a uniform distribution over (0, 1). Compute the probability that...Problem 6.53P:
Let X(1),X(2),...,X(n) be the order statistics of a set of n independent uniform (0, 1) random...Problem 6.54P:
Let Z1 and Z2 be independent standard normal random variables. Show that X, Y has a bivariate normal...Problem 6.55P:
Derive the distribution of the range of a sample of size 2 from a distribution having density...Problem 6.56P:
Let X and Y denote the coordinates of a point uniformly chosen in the circle of radius I centered at...Problem 6.61P:
Repeat Problem 6.60 when X and Y are independent exponential random variables, each with parameter...Problem 6.64P:
In Example 8b, let Yk+1=n+1i=1kYi. Show that Y1,....,Yk,Yk+1 are exchangeable. Note that Yk+1 is the...Problem 6.65P:
Consider an urn containing n balls numbered 1.. .. . n, and suppose that k of them are randomly...Problem 6.1TE:
Suppose X,Y have a joint distribution function F(x,y). Show how to obtain the distribution functions...Problem 6.4TE:
Solve Buffons needle problem when LD.Problem 6.5TE:
If X and Y are independent continuous positive random variables, express the density function of (a)...Problem 6.8TE:
Let X and Y be independent continuous random variables with respective hazard rate functions X(t)...Problem 6.9TE:
Let X1,...,Xn be independent exponential random variables having a common parameter . Determine the...Problem 6.10TE:
The lifetimes of batteries are independent exponential random variables, each having parameter . A...Problem 6.12TE:
Show that the jointly continuous (discrete) random variables X1,...,Xn are independent if and only...Problem 6.13TE:
In Example 5e t, we computed the conditional density of a success probability for a sequence of...Problem 6.14TE:
Suppose that X and Y are independent geometric random variables with the same parameter a. Without...Problem 6.15TE:
Consider a sequence of independent trials, with each trial being a success with probability p. Given...Problem 6.16TE:
If X and Y are independent binomial random variables with identical parameters n and p. show...Problem 6.17TE:
Suppose that Xi,i=1,2,3 are independent Poisson random variables with respective means i,i=1,2,3....Problem 6.19TE:
Let X1,X2,X3 be independent and identically distributed continuous random variables. Compute a....Problem 6.21TE:
Suppose that W, the amount of moisture in the air on a given day, is a gamma random variable with...Problem 6.22TE:
Let W be a gamma random variable with parameters (t,) and suppose that conditional on W=,X1,X2,...Xn...Problem 6.23TE:
A rectangular array of mn numbers arranged in n rows, each consisting of m columns, is said to...Problem 6.24TE:
If X is exponential with rate , find P{[X]=n,X[X]x} where [x] is defined as the largest integer less...Problem 6.25TE:
Suppose thatF(x) is a cumulative distribution function. Show that (a) Fn(x) and (b)1[1F(x)]n are...Problem 6.26TE:
Show that if n people are distributed at random along a road L miles long, then the probability that...Problem 6.27TE:
Suppose that X1,...,Xn are independent exponential random variables with rate A. Find a....Problem 6.28TE:
Establish Equation (6.2) by differentiating Equation (6.4).Problem 6.29TE:
Show that the median of a sample of size 2n+1 from a uniform distribution on (0, 1) has a beta...Problem 6.31TE:
Compute the density of the range of a sample of size n, from a continuous distribution having...Problem 6.32TE:
Let X(1)X(2)...X(n) be the ordered values of n independent uniform (0, 1) random variables. Prove...Problem 6.33TE:
Let X1,...,Xn be a set of independent and identically distributed continuous random variables having...Problem 6.34TE:
Let X1,....Xn, be independent and identically distributed random variables having distribution...Problem 6.37TE:
Suppose that (X,Y) has a bivariate normal distribution with parameters x,y,x,,. a. Show that...Problem 6.38TE:
Suppose that X has a beta distribution with parameters (a, b) and that the conditional distribution...Problem 6.39TE:
6.39. Consider an experiment with n possible outcomes, having respective probabilitiesProblem 6.1STPE:
Each throw of an unfair die lands on each of the odd numbers 1, 3, 5 with probability C and on each...Problem 6.2STPE:
The joint probability mass function of the random variables X,Y,Z...Problem 6.4STPE:
Let r=r1+...+rk, where all ri are positive integers. Argue that if X1,...,Xr has a multinomial...Problem 6.5STPE:
Suppose that X, Y, and Z are independent random variables that are each equally likely to be either...Problem 6.6STPE:
Let X and Y be continuous random variables with joint density functionf(x,y)={x5+cy0x1,1y50otherwise...Problem 6.7STPE:
The joint density function of X and Y isf(x,y)={xy0x1,0y20otherwise a. Are X and Y independent? b....Problem 6.8STPE:
Consider two components and three types of shocks. A type I shock causes component I to fail, a type...Problem 6.9STPE:
Consider a directory of classified advertisements that consists of m pages, where m is very large....Problem 6.10STPE:
The random parts of the algorithm in Self-Test Problem 6.9 &1 can be written in terms of the...Problem 6.12STPE:
The accompanying dartboard is a square whose sides are of length 6: The three circles are all...Problem 6.13STPE:
A model proposed for NBA basketball supposes that when two teams with roughly the same record play...Problem 6.14STPE:
Let N be a geometric random variable with parameter p. Suppose that the conditional distribution of...Problem 6.16STPE:
You and three other people are to place bids for an object, with the high bid winning. If you win,...Problem 6.17STPE:
Find the probability that X1,X2,...,Xn is a permutation of 1, 2, …., n, when X1,X2,...,Xn are...Problem 6.18STPE:
6.18. Let 4VH and Y, be independent random vectors, with each vector being a random ordering of k...Problem 6.19STPE:
Let Z1,Z2.....Zn be independent standard normal random variables, and let Sj=i=1jZi a. What is the...Problem 6.20STPE:
Let X1,X2,... be a sequence of independent and identically distributed continuous random variables....Problem 6.21STPE:
Prove the identity P{Xs,Yt}=P{Xs}+P{Yt}+P{Xs,Yt}1 Hint: Derive an expression for P{Xs,Yt} by taking...Problem 6.22STPE:
In Example 1c, find P(Xr=i,Ys=j) when ji.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
Sample Solutions for this Textbook
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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
A First Course in Probability (10th Edition)
10th Edition
ISBN: 9780134753119
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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