What are the properties of
(i) discrete random variable and
(ii) continuous random variable?

State the properties of distribution function.

A fair die is thrown. Find out the expected value of its outcomes.

Suppose the probability mass function of the discrete random variable is

X=x	0	1	2	3
p(x)	0.2	0.1	0.4	0.3

What is the value of E(3X + 2X²) ?

If f (x) is defined by f(x)=ke^-2x,  0\(\le\)x<\(\infty\) is a density function. Determine the constant k and also find mean.