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December 7th, 2011, 07:15 PM   #1
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Expectation E(X) Question

Given this pdf for a random variable X:

f(x)= { (3/4)(2x-x^2) for 0 <x < 2
0 elsewhere

What is the expected value?

I got:

Integral of x* (3/4)(2x-x^2) dx with lower limit is 0 and upper limit is 2.

So I rewrote it as:
3/4x (2x-x^2)

So the integral becomes:

6x^2 divided by 4 subtract x^3 divided by 4 dx

which becomes:
6/4 (2^3/3) - 1/4 (2^4)/4

4-1 =3

I'm confused. My textbook has 1 as the answer for the following problem. But I got a different answer. Help greatly appreciated!
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December 7th, 2011, 07:35 PM   #2
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Re: Expectation E(X) Question

I get 1 for your definite integral:



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December 8th, 2011, 01:25 PM   #3
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Re: Expectation E(X) Question

Quote:
Originally Posted by MarkFL
I get 1 for your definite integral:



How come we don't slip in the 'x' in the integral? Doesn't the expectation formula have an x in it? As in integral from minus infinity to positive infinity: xf(x) dx

Can you or someone explain why? Unless the question is subtle and the 3/4 was given as our x already.
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December 8th, 2011, 02:01 PM   #4
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Re: Expectation E(X) Question

Quote:
How come we don't slip in the 'x' in the integral?
This question is confusing. MarkFL has x inside the integral where it belongs.
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December 8th, 2011, 03:33 PM   #5
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Re: Expectation E(X) Question

Quote:
Originally Posted by mathman
Quote:
How come we don't slip in the 'x' in the integral?
This question is confusing. MarkFL has x inside the integral where it belongs.
Yes, I went ahead and factored the constant out and distributed x to f(x), giving an integrand of x(2x - x) = 2x - x.
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December 9th, 2011, 06:59 PM   #6
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Re: Expectation E(X) Question

Quote:
Originally Posted by MarkFL
Quote:
Originally Posted by mathman
Quote:
How come we don't slip in the 'x' in the integral?
This question is confusing. MarkFL has x inside the integral where it belongs.
Yes, I went ahead and factored the constant out and distributed x to f(x), giving an integrand of x(2x - x) = 2x - x.
So is it safe to say if you have a constant, its perfectly fine that you isolate it outside of the integral whenever doing these types of problems? Just want to make sure in case I run into other ones like this. Thanks for the clarification on the subtle factored in 'x'.
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December 9th, 2011, 09:04 PM   #7
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Re: Expectation E(X) Question

Yes, the following is true:

where k is a constant.
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