Discrete Random Variables (DRV) - Expectation and Variance of Discrete Random Variables
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 \(\text{P}\hspace{0.1em}\left( X=x \right)=a{{x}^{2}}\) for \(x=1,\text{}\hspace{0.5em}2,\text{}\hspace{0.5em}3,\text{}\hspace{0.5em}4\).
Find \(\text{E}\hspace{0.1em}\left( X \right)\) and \(\text{Var}\hspace{0.1em}\left( X \right)\).
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Answer:\(a=\frac{1}{30}\); \(\text{E}\hspace{0.1em}\left( X \right)=\frac{10}{3}\); \(\text{Var}\hspace{0.1em}\left( X \right)=\frac{31}{45}\)
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