5. The density function f(x) of a continuous. random variable is given below. What is the expected value of this random variable? f(x)= {19x2 when 0

(47) Let X z b(8,-) find E(5+6x) and distribution function.

Let X be a continuous random variable with PDF 3 x > 1 x4 fx(x) = otherwise Find the mean and variance of x.

c) A continuous random variable X takes values in the interval 1 < x < 3and the probability density function of x is given by: k f(x) (i) (ii) Plot the pdf of the X Show by calculation how you can determine the value of K, the expected value and the variance

A random variable X has the probability density function as                   f(x) =    Ax(9-X2)                      0 ≤ x ≤ 3                      =     0                               otherwise  Find the value of A, the mean and the standard deviation of X.

* Consider the probability density function fx (x) = a e-b lel where X is the random %3D variable which assumes all the values from (i) relation between a and b -00 to -00, Find (ii) the probability of finding X in the range 1 to 2.

Normal distribution.   The moment generating function of a random variable U is M(t) = (1 - 8t)^-7. Find: i)Probability density function, ii)Mean, iii)Variance of U.