Question

If X is a binomial random variable associated with a binomial experiment with

μ = E(X) = 54
and
σx = 6,
what are n and p?

Answer 1

For a binomial distribution over
`n` trials and with success probability
`p`, the mean
`\mu` and standard deviation
`\sigma` ar such that


`\begin{cases}\mu=np\\\sigma=√(np(1-p))\end{cases}`


`6=√(np(1-p))\implies np-np^2=36`

`54=np\implies54-54p=36\implies p=\frac13`

`54=\frac n3\implies n=162`