discrete expectation and variance

Practise discrete expectation and variance with an original VectorPaths question, worked explanation and related VCE Methods practice.

3 practice marks

Original practice question

A random variable X has distribution $P(X=0)=\frac{1}{4}$; $P(X=1)=\frac{1}{2}$; $P(X=3)=\frac{1}{4}$. Find its mean and variance.

Worked explanation

• Calculate the expectation

  $E(X)=\sum xp(x)=\frac{5}{4}$.

• Calculate the second moment

  $E(X^2)=\sum x^2p(x)=\frac{11}{4}$.

• Use the variance identity

  $\operatorname{Var}(X)=E(X^2)-[E(X)]^2=\frac{19}{16}$.

$E(X)=\frac{5}{4}$, $\operatorname{Var}(X)=\frac{19}{16}$.

Original VectorPaths practice; not an official VCAA question or marking rubric.