Recover binomial parameters from moments

Practise recover binomial parameters from moments with an original VectorPaths question, worked explanation and related VCE Methods practice.

4 practice marks

Original practice question

$X\sim\operatorname{Bin}(n,p)$ has $E(X)=6$ and $\operatorname{Var}(X)=9/2$. (a) Find p and n. [3 marks] (b) State two trial assumptions required by this model. [1 marks]

Worked explanation

• Part (a)

  $np=6$ and $np(1-p)=9/2$. Dividing gives $1-p=3/4$, so $p=1/4$ and $n=6/(1/4)=24$.

• Part (b)

  The fixed 24 trials must be independent, with the same success probability on each trial; each trial has success or failure as its two outcomes.

(a) $p=1/4$, $n=24$.; (b) Independent trials; constant success probability.

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