• Problem 3: Find the expected value of the function g(X) = X³ where X is a random variable defined by the density f.(x) = (0.5) u(x) ew2) %3D

4. The monthly revenue (in millions) of a local gaming company is represented by a continuous random variable X having the probability density f(x) = (1 - (x-1)²), 0 < x < 2, 0, elsewhere Find the mean and variance of X.

4. A continuous random Variable X has probability Density function defined by f(x) = 5-5x; 0<=x<=1, =0 otherwise, find the mean and the variance of the distribution.

We have a random variable X and Y that jave the joint pdf f(x) = {1    0<x<1, 0<y<1}                                                                                                                                                            {0         otherwise} If  U = Y-X2 , what is the support for the random variable U? What would fu(u) and Fu(u) be? Say  U = Y/X, what is the support for the random variable U? What would fu(u) and Fu(u) be?

i need help

PLEASE SOLVE BOTH PARTS:

3) (20 points) A random variable X has density function given by x20 f(x) = 1)

2. Let X be a random variable with density function ) = √(2x² - + f(x) = Find the expected value of g(x) = 2X+1. 8x2 +5x + 6), 1 < x < 2, 0, elsewhere