Binomial Second Moment

[apricimo]

Hi

 

I was wondering how come when they show the calculation of a second moment for a particular variable they don't also square the binomial function but only the term outside it.

 

for example this is how they show it

 

[math]

 

 

\begin{array}{l}

\overline {n_1 ^2 } = \sum\limits_{n = 0}^M {W(n_1 )} n_1 ^2 \\

\overline {n_1 ^2 } = \sum\limits_{n = 0}^M {\frac{{N!}}{{n_1 !(N - n_1 )!}}p^{n_1 } q^{N - n_1 } } n_1 ^2 \\

\end{array}

 

[/math]

 

why not also square the n inside the W function?

[timo]

Given a probability function P(x) and a function f(x), then the expectation value for f is [math] \bar f = \sum_x P(x)f(x)[/math]. The second moment is the expectation value for the "function" f(x)=x², i.e. [math] \overline{x^2} = \sum_x P(x) x^2[/math].

[apricimo]

Given a probability function P(x) and a function f(x), then the expectation value for f is [math] \bar f = \sum_x P(x)f(x)[/math]. The second moment is the expectation value for the "function" f(x)=x², i.e. [math] \overline{x^2} = \sum_x P(x) x^2[/math].

 

 

ah oh ok

 

thank you