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 $P(X=0)=\frac{1}{5}$; $P(X=2)=\frac{1}{2}$; $P(X=5)=\frac{3}{10}$. Find its mean and variance.

Worked explanation

• Calculate the expectation

  $E(X)=\sum xp(x)=\frac{5}{2}$.

• Calculate the second moment

  $E(X^2)=\sum x^2p(x)=\frac{19}{2}$.

• Use the variance identity

  $\operatorname{Var}(X)=E(X^2)-[E(X)]^2=\frac{13}{4}$.

$E(X)=\frac{5}{2}$, $\operatorname{Var}(X)=\frac{13}{4}$.

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