
A continuous random.variable X was found to have the following densi function: 4Q3y3 + 47) Oaxs...
Q 2. The probability density function of the continuous random variable X is given by Shell, -<< 0. elsewhere. f(x) = {&e*, -40<3<20 (a) Derive the moment generating function of the continuous random variable X. (b) Use the moment generating function in (a) to find the mean and variance of X.
2x 0<x<1 Let X be a continuous random variable with probability density function f(x)= To else The cumulative distribution function is F(x). Find EX.
4. Let X and Y have joint density function le-x 0 < y < x < 0 Jxy(x, y) = lo elsewhere Another random variable of interest is U=X–Y. Find the probability density function for U.
Let X and Y be two continuous random variables having the joint probability density 24xy, for 0 < x < 1,0<p<1.0<x+y<1 0, elsewhere Find the joint probability density of Z X + Y and W-2Y.
b. Let X be a continuous random variable with probability density function f(x) = kx2 if – 1 < x < 2 ) otherwise Find k, and then find P(|X| > 1/2).
4. Let X be a continuous random variable with probability density function: x<1 0, if if| if x>4 f(x) = (x2 + 1), 4 x 24 0 Find the standard deviation of random variable X.
Question #37 Let X be a continuous random variable with the following density function: p(-x+ /2) for - 0<x<00. Calculate E[X | X > 0). Possible Answers B 1/727 © 12 D/2TR Ⓡ 1.00
2. Le X be a continuous random variable with the probability density function x+2 18 -2<x<4, zero otherwise. Find the probability distribution of Y-g(X)- XI
1. A continuous random variable has probability density function f(x) = 2x for all 0 < x < 1 and f(x) = 0 for all other 2. Find Prli <x< 1. O 1 16 O OP O . O 1
x(3-x) 0<x<3 Let X be a continuous random variable with density function What is the mode of X. Answer in simplied fraction form