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 Jaket1 October 23rd, 2017 04:38 AM

expectation question help

if u=expectation(x) find expectation(x^2)

would the answer just be u^2 or do i need more information, thanks!

 Joppy October 23rd, 2017 05:01 AM

Is that the entire question? We could possibly express $E(X^2)$ in terms of the variance. But I've been wrong before :p.

$\sigma_X^2 = E(X^2) - \mu_X^2 \implies E(X^2) = \sigma_X^2 + \mu_X^2$

And no, E(X^2) definitely does not equal E(X)^2 !

 Jaket1 October 23rd, 2017 06:08 AM

Thankyou! The question actually is this: https://imgur.com/a/YbZw2 so i expanded out the rth moment of skewness and was wondering how i could elimate the e(x^2) and e(x) terms so ur reply helps a lot. :)

 Jaket1 October 23rd, 2017 06:16 AM

thanks i have completed the question :p

 Country Boy October 23rd, 2017 10:59 AM

Example: Suppose x can take on the values 0, 1, and -1 with probability 1/3 each. Then the expected value of x is E(x)= -1(1/3)+ 0(1/3)+ 1(1/3)= 0.

u= x^2 takes on the values 0^2= 0, 1^2= 1 and (-1)^2= 1 with probability 1/3 each. That is the same as saying "0 with Probability 1/3 and 1 with probability 2/3". The expected value of u= x^2 is E(u)= 0(1/3)+ 1(2/3)= 2/3.

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