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October 23rd, 2017, 05:38 AM   #1
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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!
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October 23rd, 2017, 06:01 AM   #2
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Math Focus: Yet to find out.
Is that the entire question? We could possibly express $E(X^2)$ in terms of the variance. But I've been wrong before .

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

And no, E(X^2) definitely does not equal E(X)^2 !
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October 23rd, 2017, 07:08 AM   #3
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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.
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October 23rd, 2017, 07:16 AM   #4
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thanks i have completed the question
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October 23rd, 2017, 11:59 AM   #5
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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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