# Math Help - prove or disprove Variance = p(1-p) for bernoulli mass function

1. ## prove or disprove Variance = p(1-p) for bernoulli mass function

given Ber(x,p) = Pr(X=x) = {p , x=1
{1-p , x=0
{ o , else

Let p e(0,1) and X~Ber(x,p). Prove or disprove that Var[x]= p(1-p).

no idea where to start on this one guys...

2. Originally Posted by nikie1o2
given Ber(x,p) = Pr(X=x) = {p , x=1
{1-p , x=0
{ o , else

Let p e(0,1) and X~Ber(x,p). Prove or disprove that Var[x]= p(1-p).

no idea where to start on this one guys...

$\text{Var}(x)=E((x-\overline{x})^2)$

We have $\text{Pr}(X=1)=p,\ \text{Pr}(X=0)=1-p$ and all other values have probability zero.

So:

$\overline{x}=E(x)=(1\times p) + (0 \times (1-p))=p$

and:

$E((x-\overline{x})^2)=(1-p)^2 \times p+(0-p)^2\times (1-p)=..$

CB