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- October 31st 2006, 09:27 AM #1
## E(X) and Var(X)

1. The random variable X has pdf fX(x) = x^−4for x > 1, and 0, otherwise.

(a) Compute E(X) and Var(X).

(b) Let Y =√X. Compute E(Y ) and Var(Y ).

(c) Let W = 2X + 5. Compute E(W) and Var(W).

By the way, how do I get the Math symbols to work while pasting directly from my Words? Thanks

- October 31st 2006, 10:22 AM #2

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- October 31st 2006, 02:13 PM #3

That's why I couldn't get the answer at all. I emailed my prof this morning. He just replied saying there's a typo. The correct question is

1. The random variable X has pdf fX(x) = 3x^−4for x > 1, and 0, otherwise.

(a) Compute E(X) and Var(X).

(b) Let Y =√X. Compute E(Y ) and Var(Y ).

(c) Let W = 2X + 5. Compute E(W) and Var(W).

Does the 3 make a difference?

- October 31st 2006, 02:22 PM #4

- October 31st 2006, 04:06 PM #5

Answers:

a) E(X) = 3/2, E(X^2)=3, Var(X)=3/4

b) Can someone help me with this please? All the questions I did before was when X ~Unif(0,1). How do you do it for this when it's not

unif(0,1)? Thanks

c) Using the the values I got from a), I got E(W)=3 and Var(W)=3. ----> Can the expected value and variance be the same?

E(W) = 2E(X) = 2(3/2) = 3. Var(X) = 2^2Var(X) = 4Var(X) = 4(3/4) = 3.

The answers look so wrong though. Did I do something wrongly? I just integrated with the formula my prof gave.

Thanks in advance.

- October 31st 2006, 04:14 PM #6

- October 31st 2006, 08:36 PM #7

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- October 31st 2006, 09:22 PM #8
Thank you very much.

Arg.....shows how much i understand probability when I don't even know that I'm supposed to use the pdf from part a). Arg.....

Question: Therefore it doesn't matter that if X~unif(0,1)? I just need to use the pdf? Then integrate from whatever values that are given? The unif(0,1) is to integrate values from 0 to 1? If for eg, if not uniform, values given are 2<x<7, just need to integrate from 2 to 7?

- October 31st 2006, 10:36 PM #9

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- November 1st 2006, 08:41 AM #10