2. Suppose a r.v. X has the density function 2 x, for 0<x<1 f(x) = 10,...
Let X be a r.v. with probability density function f(x)-e(4-x2), -2 < otherwise (a) What is the value of c? (b) What is the cumulative distribution function of X? (c) What is EX) and VarX
Suppose that the probability density function of X is f(x) {cx3 0 1< x < 5 otherwise where c is a constant. Find P(X < 2).
Suppose that the probability density function of X is f(x) {cx3 0 1< x < 5 otherwise where c is a constant. Find P(X < 2).
Suppose that X has the probability density function f(x) = { 2x 0 < x < 1 0 otherwise Which of the following is the moment generating function of X? 2 et t 2 et t2 2 t2 O t2 2 eet t 2 ett t2 t e eut-1 t
2. Let X and Y have joint density f(x.v) = \ şcy? if 0 <x< 1 and 1 <y<2, otherwise. (a) Compute the marginal probability density function of Y. If it's equal to 0 outside of some range, be sure to make this clear. (b) Set up but do not compute an integral to find P(Y < 2X).
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).
Suppose that X and Y are jointly continuous random variables with joint probability density function f(x,y) = {12rºy, 1 0, 0<x<a, 0<y<1 otherwise i) Determine the constant a ii) Find P(0<x<0.5, O Y<0.25) HE) Find the marginal PDFs fex) and y) iv) Find the expected value of X and Y. Le. E(X) and E(Y) v) Are X and Y independent? Justify your answer.
Suppose that the probability density function of X is f(x) {cx3 0 1< x < 5 otherwise where c is a constant. Find P(X < 2).
Suppose that the probability density function of X is f(x) {cx3 0 1< x < 5 otherwise where c is a constant. Find P(X < 2).
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.