The entire area of f(x) should be 1. Hence,
k*() = 1
k = 1/
5. Given the probability density f(x)= for -0<x<00, find k. 1+ 2 Jor -
The probability density function of X is given by 0 elsewhere Find the probability density function of Y = X3 f(r)-(62(1-x)for0 < x < 1
7. For the probability density function f(x) = for 0 <<<2 (a) Find P(x < 1) (b) Find the expected value. (c) Find the variance.
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).
3,40 A random variable X has probability density function fx(x) = 1 0<x< 1. Find the probability density function of Y = 4x3 - 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 the probability density function of X is f(x) {cx3 0 1< x < 5 otherwise where c is a constant. Find P(X < 2).
(1 point) The joint probability density function of X and Y is given by f(x, y) = cx – 16 c”, - <x< 0 < b < co alt 0 < y < 0 Find c and the expected value of X: c = E(X) =
2.5.6. The probability density function of a random variable X is given by f(x) 0, otherwise. (a) Find c (b) Find the distribution function Fx) (c) Compute P(l <X<3)
(8pts) 1. The joint probability density of X and Y is given by + 0<x<1 and 0 <y< 2 otherwise a) Verify that this is a joint probability density function. b) Find P(x >Y). o) Find Pſy > for< d) Find Cov(X,Y). e) Find the correlation coefficient of X and Y (Pxy).