- #1

- 10

- 0

## Homework Statement

X

_{1},X

_{2},...,X

_{k}~iid Bin(n,p) find the MME (Method of Moments Estimator) for p

## Homework Equations

E[X] = n⋅p

Var[X] = n⋅p⋅(1-p)

Var(X) = E[X

^{2}] - [E[X]]

^{2}

## The Attempt at a Solution

Does this look correct?

n⋅p⋅(1-p) = E[X

^{2}] - n

^{2}⋅p

^{2}

E[X

^{2}] = n⋅p⋅(1-p) + n

^{2}⋅p

^{2}

[itex]\bar{X}[/itex]=n⋅p

[itex]\bar{X}[/itex]

^{2}= n⋅p⋅(1-p) + n

^{2}⋅p

^{2}

[itex]\bar{X}[/itex]

^{2}= [itex]\bar{X}[/itex]⋅(1-p) + [itex]\bar{X}[/itex]⋅[itex]\bar{X}[/itex]

[itex]\hat{p}[/itex] = (([itex]\bar{X}[/itex])

^{2}+ [itex]\bar{X}[/itex] - [itex]\bar{X}[/itex]

^{2}) / [itex]\bar{X}[/itex]

Thanks.

Last edited: