9. Two discrete random variables X and Y have joint probability mass function (pmf) 1,2,...,n; y = 1, 2, . . . , x. f(x) = { k n(n+1) 0 Xx = otherwise (d) Use the fact that E(Y) = Ex (Ey\x(Y|X)), where Ex( ) and Ey|x( ) are the expected values with respect to X and with respect to Y given X, respectively, to show that E(Y) = n(n+³) 4

9. Two discrete random variables X and Y have joint probability mass function (pmf) 1,2,...,n; y = 1, 2, . . . , x. f(x) = { k n(n+1) 0 Xx = otherwise (d) Use the fact that E(Y) = Ex (Ey\x(Y|X)), where Ex( ) and Ey|x( ) are the expected values with respect to X and with respect to Y given X, respectively, to show that E(Y) = n(n+³) 4

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

Q3// let X and Y have the joint probability distribution function as : . (x, y) (1,1) (1,2) (1,3) p(x,y) 2/15 4/15 3/15 and p(x, y) is equal to zero elsewhere. (2,1) 1/15 (2,2) 1/15 (2,3) 4/15 a. Find the means μ₁, ₂, the variance of, o2, and the correlation coefficients p, then describe the relation between x and y. b. Compute μ₂ + p(0²/0₁)(x-μ₁)
d) The random variable X has a Poisson distribution such that P(X= 0) = P(X = 1). Calculate P(X = 2).
(1) Let X be a random variable with p.d.f. 1-8x 0
and variance of X if the probability mass function is f(x) = ; ;)" , Find the moment generating function, mean x = 1, 2, 3, 4, ...
2. (5 ts) Suppose X is a discrete random variable with probability mass function (pmf) f(x) = c(x - 1)2 for r= -4,-2,2,4, | where c is a constant. (a) Find c. (b) Find P(-2 < X < 5).
(1) Let X = b(16, -) find E(4-3x) and distribution function. (2) Let X be a random variable with p.d.f. -2 kx 1
7 Find the expected value of the function g (X) = X², where x is a random variable defined by the đensity, fx ) = a. eax, u u (x), where 'a' is a constant.
2. The discrete random variable X has the probability function kx, P(X = x) = }k(x – 2), 0, x = 2,4,6 x = 8 otherwise Where k is a constant. (a) Show that k %3D 18 (b) Find the exact value of F(5).
Suppose that the random variables X and Y have the following joint probability density function. f(x, y) = ce-8x - 5y, 0 0).