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#1




SOA #28
Hello,
Can someone please advise me if I can use the following formula (instead of the simple integration) to answer SOA #28? E[X^a] = (u^3  d^3) / 3 (u  d) Where u is the high end of each interval and d is the low end of each interval? Thank you!
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#2




You would get a quicker response if you would post the question.

#4




Quote:
Did you mean to perhaps substitute the 3's on the right hand side with a's? 
#6




Yes, the correct approach is to use E[X^2] = (b^3  a^3) / (3(ba)) for each interval. For the limited expected value piece, first rewrite the intervals with a maximum value of 150. Just be sure to weight the intervals by their empirical probabilities.
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#7




Your formula gives a conditional expectation: E[X^2 d < X < u]

#8




Quote:
Thank you for the response. I did try that but could not seem to get the right answer. For the last part of the interval above 150 would it be: [3 * (150^2)]/78? Thank you!
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#9




Thank you for posting the question, bravesandFalcons!
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#10




Yes, the last part is a little different because you are essentially going from 150 to 150. So it is E[X^2] = 150^2. Or think of E[X^2] as Var(X) + E[X]^2. The variance of 150 here is 0. The expected value is 150^2. Weight this with 3/74.
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