Expectation of standardised random variable

[IvanCarrie]

Given

\(\displaystyle U=\frac{X-EX}{\sigma_X} \)

so

\(\displaystyle E = 0 \)

how does

\(\displaystyle E[U^2] = 1 \) ?

 

[tkhunny]

Given

\(\displaystyle U=\frac{X-EX}{\sigma_X} \)

so

\(\displaystyle E = 0 \)

how does

\(\displaystyle E[U^2] = 1 \) ?

\(\displaystyle U^{2} = \left(\dfrac{X - E[X]}{\sigma_{X}}\right)^{2}\) --Can you prove it?

 

[HallsofIvy]

\(\displaystyle \frac{3}{3{\int_{-1}^1 x dx= 0\) but \(\displaystyle \frac{3}{2}\int_{-1}^1 x^2 dx= 1\).