2.6.17. The probability density function of the random variable X is given by 6x-21-3 -, 2<x<3...
2.6.17. The probability density function of the random variable X is given by r2 21 0<x-1, 6x-2r2-3 (x, 3)2 0 otherwise.
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)
Problem #2: Suppose that a random variable X has the following probability density function. SC(16 - x?) 0<x< 4 f(x) = 3 otherwise Find the expected value of x.
2. Suppose X is a continuous random variable with the probability density function (i.e., pdf) given by f(x) - 3x2; 0< x < 1, - 0; otherwise Find the cumulative distribution function (i.e., cdf) of Y = X3 first and then use it to find the pdf of Y, E(Y) and V(Y)
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.
Suppose that X is a continuous random variable whose probability density function is given by (C(4x sa f(x) - 0 otherwise a) What is the value of C? b) Find PX> 1)
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
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).
The random variable X has the probability density function (x)a +br20 otherwise If E(X) 0.6, find (a) P(X <름) (b) Var(x)
3) The continuous random variable X has the probability density function, ), 2 3x3 f(x) = { a, 35x55 2 - bx, 5 < x < 6 elsewere 10 i)Find the value of a and b and hence, sketch f(x) ii) Find the cumulative distribution function, f(x) and sketch it.