Chapter 5.5, Problem 64E

i.

To determine

To prove: that $E\left({\left(x-\mu \right)}^2\right)=E\left(x^2-2\mu x+{\mu }^2\right)$ .

ii.

To determine

To prove: that $E\left(x^2-2\mu x+{\mu }^2\right)=E\left(x^2\right)-E\left(2\mu x\right)+E\left({\mu }^2\right)$ .

iii.

To determine

To prove: that $E\left(x^2\right)-E\left(2\mu x\right)+E\left({\mu }^2\right)=E\left(x^2\right)-2E\left(\mu \right)E\left(x\right)+E{\left(x\right)}^2$ .

iv.

To determine

To prove: that $E\left(x^2\right)-2E\left(\mu \right)E\left(x\right)+E{\left(x\right)}^2=E\left(x^2\right)-2E{\left(x\right)}^2+E{\left(x\right)}^2$ .

v.

To determine

To prove: that $E\left(x^2\right)-2E{\left(x\right)}^2+E{\left(x\right)}^2=E\left(x^2\right)-{\mu }^2$ .