Chapter 2.3, Problem 2E

For each of the following distributions, find $\mu =E\left(X\right),E\left[X\left(X-1\right)\right]$, and ${\sigma }^2=E\left[X\left(X-1\right)\right]+E\left(X\right)-{\mu }^2$

(a) $f\left(x\right)=\frac{3!}{x!\left(3-x\right)!}{\left(\frac{1}{4}\right)}^x{\left(\frac{3}{4}\right)}^{3-x},x=0,1,2,3.$

(b) $f\left(x\right)=\frac{4!}{x!\left(4-x\right)!}{\left(\frac{1}{2}\right)}^4,x=0,1,2,3,4.$