Unknown probability, expectation and variance

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

4 practice marks

Original practice question

A random variable X takes values 0, 2 and 4 with probabilities $k$, $2k$ and $k$, respectively. (a) Find k and E(X). [2 marks] (b) Find Var(X). [2 marks]

Worked explanation

• Part (a)

  The probabilities sum to $4k=1$, so $k=1/4$. Then $E(X)=0/4+2/2+4/4=2$.

• Part (b)

  $E(X^2)=0+4(1/2)+16(1/4)=6$. Hence $\operatorname{Var}(X)=6-2^2=2$.

(a) $k=1/4$, $E(X)=2$.; (b) $2$.

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