Probability Mass Function given by f(x) = c(x^2 + 4), where

[abc4616]

The P.M.F. (probability mass function) of a discrete random variable X is given by f(x) = c(x^2 + 4), where X = (0, 1, 2, 3), and c is a constant.

a) Determine value of c.
b) Find the mean and variance of X.

Does anyone know how to answer this?

 

[pka]

Solve the equation $\displaystyle \sum\limits_{k = 0}^3 {f(k)} = 1$ for c.

The expected value (the mean) is $\displaystyle E(X) = \sum\limits_{k = 0}^3 {k\;f(k)} .$

The variance is $\displaystyle V(X) = \sum\limits_{k = 0}^3 {k^2 f(k) - \left( {E(X)} \right)^2 }.$

 

[abc4616]

Thank You for the help