Discrete Random Variables (DRV) - Expectation and Variance of Discrete Random Variables

IB AA SL: core and optional content

Core: normalization and expectation. Optional: variance.

A random variable \(X\) takes integer values between \(1\) and \(4\) inclusive where \(\mathrm{P}\left( X=x \right)=a x^{3}+0.01\) for \(x=1,\ 2,\ 3,\ 4\).

Find \(\mathrm{E}\left( X \right)\) and \(\mathrm{Var}\left( X \right)\).