Chapter 8.2, Problem 43E

To determine

(a).

To show:

The relation $E\left(c\right)=c$, if $X$ and $Y$ are random variables and $c$ is any constant.

To determine

(b).

To show:

The relation $E\left(cX\right)=cE\left(X\right)$ if $X$ and $Y$ are random variables and $c$ is any constant.

To determine

(c).

To show:

That $E\left(X+Y\right)=E\left(X\right)+E\left(Y\right)$ if $X$ and $Y$ are random variables and $c$ is any constant.

To determine

(d).

To show:

That $E\left(X-Y\right)=E\left(X\right)-E\left(Y\right)$ if $X$ and $Y$ are random variables and $c$ is any constant.