Suppose a random variable X has athe following probability d

Suppose a random variable X has athe following probability density function:

0 < x < infinity

zero otherwise

----------

a) Find the value of C that would make f(x) a valid probability density function.

b) Find the median of the probability distribution of X.

c) Find the mean of the probability distribution of X.

d) Find the variance of the probability distribution of X.

e) Find the moment-generating function of X, M_x(t). For which values of t does it exist?