Discrete Random Variables (DRV)

IB AA SL: core and optional content

Core: use normalization and expectation to find a,b. Optional: variance.

A random variable \(X\) takes integer values between \(2\) and \(5\) inclusive where \(\text{P}\hspace{0.1em}\left( X=x \right)=ax+b\) for \(x=2,\text{}\hspace{0.5em}3,\text{}\hspace{0.5em}4,\text{}\hspace{0.5em}5\). Given that \(\text{E}\hspace{0.1em}\left( X \right)=3.85\), find the values of \(a\), \(b\) and \(\text{Var}\hspace{0.1em}\left( X \right)\).