EBK FIRST COURSE IN PROBABILITY, A
10th Edition
ISBN: 9780134753676
Author: Ross
Publisher: PEARSON CUSTOM PUB.(CONSIGNMENT)
expand_more
expand_more
format_list_bulleted
Question
Chapter 6, Problem 6.46P
To determine
To find: Conditional distribution of Y.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Let X - U[0, 1]. Find the distribution of Y = 1 - X.
Prove the memoryless property of Expoential Distribution.
Hint: Prove that For X-exponential(X) and any two positive real numbers a and y, P(X2x+y₁ X 2 x) = P(X ≥ 1).
Fx (x)=0, x ≤ 0; Fx (x) = 1 -e-, a > 0.
For the joint distribution function
f(x,y)=2 for x≥0,y≥0,x+y≤1 and 0 otherwise
Find the marginal of X and Y.
Are X and Y independent?
Find E(X )
Chapter 6 Solutions
EBK FIRST COURSE IN PROBABILITY, A
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 - Let X1 and X2 be independent normal random...Ch. 6 - Prob. 6.34PCh. 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. 6.41PCh. 6 - Prob. 6.42PCh. 6 - Prob. 6.43PCh. 6 - The joint probability mass function of X and Y is...Ch. 6 - Prob. 6.45PCh. 6 - Prob. 6.46PCh. 6 - An insurance company supposes that each person has...Ch. 6 - If X1,X2,X3 are independent random variables that...Ch. 6 - Prob. 6.49PCh. 6 - If 3 trucks break down at points randomly...Ch. 6 - Consider a sample of size 5 from a uniform...Ch. 6 - Prob. 6.52PCh. 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. 6.57PCh. 6 - Prob. 6.58PCh. 6 - Prob. 6.59PCh. 6 - Prob. 6.60PCh. 6 - Repeat Problem 6.60 when X and Y are independent...Ch. 6 - Prob. 6.62PCh. 6 - Prob. 6.63PCh. 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. 6.2TECh. 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 - 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. 6.30TECh. 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. 6.35TECh. 6 - Prob. 6.36TECh. 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. 6.40TECh. 6 - Prob. 6.41TECh. 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...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. 6.24STPECh. 6 - Prob. 6.25STPECh. 6 - Let X1,...,Xn, be independent nonnegative integer...
Knowledge Booster
Similar questions
- Check whether X and Y are independent if their jointprobability distribution is given by(a) f(x, y) = 1 4 for x = −1 and y = −1, x = −1 andy = 1, x = 1 and y = −1, and x = 1 and y = 1;(b) f(x, y) = 1 3 for x = 0 and y = 0, x = 0 and y = 1, and x = 1 and y = 1.arrow_forwardObtain regression curve of Y on X for the following distribution: y y ƒ(x, y) = (1 + 6 exp(- / +)* x)² 1 x ; x, y 20arrow_forwardLet x and y be joint continuous random variable with joint pdf f XY (x, y) = {?x + 1 , x, y ≥ 0, x + y < 10, ??ℎ??????1. Find the constant c.2. Find the marginal PDF’S fX (x) and fY (y)3. Find P(Y<2X2)arrow_forward
- Let X = N(u,0²), let Y=2X+b, b0, then distribution of Y isarrow_forwardLet X be a random variable with uniform distribution on the interval [-2,2]. Let Y be defined as Y = X5. Calculate the pdf of Y.arrow_forwardFind the average temperature in the box D={(x,y,z): 0≤x≤ In 3, 0sys In 9, 0≤z≤ In 27) with a temperature distribution of T(x,y,z)= 18 e*-y-². The average temperature is (Type an exact answer.) ***Parrow_forward
- Let X and Y be jointly continuous random variables with joint PDF cx +1, 2,y> 0, x+ y<1 0, fx,x (x, y) = otherwise. Then the constant c= And the probability that P(Y < 2X²) = ;: Here a = and b =arrow_forwarda) compare E(Y|X=x) and E(Y|X) b) Find the pdf of Y c) find the conditional pdf of X given that Y=yarrow_forwardA random point (X, Y) is drawn from the triangle below. The has the characteristic that the conditional expected value E(X|Y)=0 for all YE[0,2]. (X, Y) a. Determine the expected value E(X) and E(XY) b. Give an example of a pdf f(x,y) so that the simultaneous distribution have the specified characteristic.arrow_forward
- Assume that X1, X2, X3 ∼ Exp (λ) are independent and evenly distributed with the distribution Exp (λ = 1). (a) Determine the distribution of Y = X1 + X2 + X3 and state its PDF f (y). (b) Determine the distribution of U = 2Yarrow_forward3. Let X be a continuous random variable on the interval [0, 1] having cdf Fx(x) = 3x² − 2x³. Let W = 4 + 3X. (a) What is the range of W? (b) Find a formula for Fw(w). (c) Find a formula for fw(w).arrow_forwardConsider X and Y are joint distributed with PDFf(x,y)=x+y, 0≤x≤1, 0≤y≤1. (d) Find the marginal distributions of X and Y .(e) Find the conditional distribution of X given Y = y.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
A First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON
A First Course in Probability (10th Edition)
Probability
ISBN:9780134753119
Author:Sheldon Ross
Publisher:PEARSON