Chapter 1.6, Problem 12E

a.

To determine

Verify that the mean value, variance, and standard deviation of the statistical population $w_1,\dots ,w_N$ are ${\mu }_w=c_1+{\mu }_v$, ${\sigma }_w^2={\sigma }_v^2$, and ${\sigma }_w={\sigma }_v$, respectively.

b.

To determine

Verify that the mean value, variance, and standard deviation of the statistical population $w_1,\dots ,w_N$ are ${\mu }_w=c_2{\mu }_v$, ${\sigma }_w^2=c_2^2{\sigma }_v^2$, and ${\sigma }_w=\left|c_2\right|{\sigma }_v$, respectively.

c.

To determine

Verify that the mean value, variance, and standard deviation of the statistical population $w_1,\dots ,w_N$ are ${\mu }_w=c_1+c_2{\mu }_v$, ${\sigma }_w^2=c_2^2{\sigma }_v^2$, and ${\sigma }_w=\left|c_2\right|{\sigma }_v$, respectively.