Expectation of standardised random variable

IvanCarrie

New member
Joined
Jan 2, 2019
Messages
4
Given

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

so

\(\displaystyle E = 0 \)

how does

\(\displaystyle E[U^2] = 1 \) ?
 

tkhunny

Moderator
Staff member
Joined
Apr 12, 2005
Messages
10,675
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

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Jan 27, 2012
Messages
6,029
\(\displaystyle \frac{3}{3{\int_{-1}^1 x dx= 0\) but \(\displaystyle \frac{3}{2}\int_{-1}^1 x^2 dx= 1\).
 
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