Chapter 2.3, Problem 1E

Find the mean, variance, and index of skewness for the following discrete distributions:

(a) $f\left(x\right)=1,x=5$

(b) $f\left(x\right)=\frac{1}{5},x=1,2,3,4,5.$

(c) $f\left(x\right)=\frac{1}{5},x=3,5,7,9,11.$

(d) $f\left(x\right)=\frac{x}{6},x=1,2,3.$

(e) $f\left(x\right)=\frac{\left(1+\left|x\right|\right)}{5},x=-1,0,1.$

(f) $f\left(x\right)=\frac{\left(2-\left|x\right|\right)}{4},x=-1,0,1.$