3. Suppose that three random variables X1, X2, and X3 have a continuous joint distribution with the following joint p.d.f.: f(x1, x2, x3) = ce-(x1+2x2+3x3) for x; > 0 (i =1, 2, 3), otherwise. Determine (a) the value of the constant c; (b) the marginal joint p.d.f.of X1 and X3; and (c) Pr(X1 < 1|X2 =2, X3=1).

3. Suppose that three random variables X1, X2, and X3 have a continuous joint distribution with the following joint p.d.f.: f(x1, x2, x3) = ce-(x1+2x2+3x3) for x; > 0 (i =1, 2, 3), otherwise. Determine (a) the value of the constant c; (b) the marginal joint p.d.f.of X1 and X3; and (c) Pr(X1 < 1|X2 =2, X3=1).

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Similar questions

8. Be X a discrete random variable with distribution given by: Select one: a. 1/8 b. 1/4 c. 3/8 d. 5/8
4. Let X₁ N (0,3²), X₂ N(4,4²), and X3 ~ N(-1,22) be independent random variables. Find P (X₁ + X₂ +3X3 <-8), using the table for standard normal distribution.
1.) The amount of time an air-conditioning technician to repair a unit is in between 1.9 and 5 hours which is found to be uniformly distributed. Let x be the time needed to fix an A/C unit. b.) Find the probability that a randomly selected A/C unit repair requires less than 3.5 hours?
1. Let X1, X,.., X, random sample from distribution be a a Geometric 2....., fx (x) = p(1– p)*| F, (y,) = ? x-1 x=1,2,3,.... Fy, (y,) = ? P(Y, <1) =? а. b. С.
Ee.6.
Suppose X is a random variable of uniform distribution between 1 and 7. Find E(X)
9. Given that f(x, y) = (2x+2y)/2k if x = 0,1 and y = 1,4, is a joint probability distribution function for the random variables X and Y. Find: (f(x|y = 1)
25. Let X have a three-dimensional normal distribution with mean vector and covariance matrix and A- 3-1 respectively. Set Y= X1 +X + X, and Y= X1+X. Determine the conditional distribution of Y given that Y 0.
55. Given this joint pmf, (a) Find the conditional distribution of X given Y = 0, fxY=0(x) = P(X=x|Y = 0). (b) Are X and Y independent? Justify your answer.
2. Suppose that X and Y are independent random variables, both with the standard normal distribution i.e. X, Y~ N(0, 1). For pe [-1, 1], define Z:=√1-p²X + pY. Show that E[Z|Y] =pY.
Let X1, X2, X3, be a r. s. from normal distribution with mean 0 and variance 1, let the prior distribution of 0 is normal with mean zeroand variance 1. Let L(6,0) = (ô - 0). Find the Bayes estimator of 0
5. Let (*1, x2, .., rn) be n independent random sample of size n from a uniform distribution on the interval [01,02]; (a) find the c.d.f of, X(1), the minimum order statistic (b) find the c.d.f of, X(n), the maximum order statistic (c) Hence, find the mean and variance of X(1) and X(n)-