Hello,
I am stuck trying to calculate the second moment of the geometric distribution.
E(x^2) = Sum (x^2 * f(x))
= Sum (x^2 * p * q^(x-1))
I am not sure how to progress further from here - do you have any pointers? Thanks
Hello,
I am stuck trying to calculate the second moment of the geometric distribution.
E(x^2) = Sum (x^2 * f(x))
= Sum (x^2 * p * q^(x-1))
I am not sure how to progress further from here - do you have any pointers? Thanks
What about
$\displaystyle \displaystyle E(x^2)=\sum_{x=1}^\infty x^2 p q^{x-1}=\sum_{x=1}^\infty x p \frac{d}{dq} q^x=\frac{d}{dq}\sum_{x=1}^\infty x p q^x}=\frac{d}{dq} \Big(q E(x)\Big)=\ldots$
Since you know the value of the first moment, $\displaystyle E(x)$, you are essentially done.