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October 23rd, 2017, 04:38 AM  #1 
Member Joined: Jan 2016 From: Blackpool Posts: 97 Thanks: 2  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! 
October 23rd, 2017, 05:01 AM  #2 
Senior Member Joined: Feb 2016 From: Australia Posts: 1,643 Thanks: 571 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 ! 
October 23rd, 2017, 06:08 AM  #3 
Member Joined: Jan 2016 From: Blackpool Posts: 97 Thanks: 2 
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. 
October 23rd, 2017, 06:16 AM  #4 
Member Joined: Jan 2016 From: Blackpool Posts: 97 Thanks: 2 
thanks i have completed the question 
October 23rd, 2017, 10:59 AM  #5 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,261 Thanks: 894 
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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