My Math Forum Expectation E(X) Question

 December 7th, 2011, 07:15 PM #1 Newbie   Joined: Oct 2011 Posts: 22 Thanks: 0 Expectation E(X) Question Given this pdf for a random variable X: f(x)= { (3/4)(2x-x^2) for 0
 December 7th, 2011, 07:35 PM #2 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs Re: Expectation E(X) Question I get 1 for your definite integral: $\frac{3}{4}\int_0\,^2 2x^2-x^3\,dx=\frac{3}{4}$\frac{2}{3}x^3-\frac{1}{4}x^4$_0^2=\frac{3}{4}$$\frac{16}{3}-\frac{16}{4}$$=$ $12$$\frac{1}{3}-\frac{1}{4}$$=\frac{12}{12}=1$
December 8th, 2011, 01:25 PM   #3
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Re: Expectation E(X) Question

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 Originally Posted by MarkFL I get 1 for your definite integral: $\frac{3}{4}\int_0\,^2 2x^2-x^3\,dx=\frac{3}{4}$\frac{2}{3}x^3-\frac{1}{4}x^4$_0^2=\frac{3}{4}$$\frac{16}{3}-\frac{16}{4}$$=$ $12$$\frac{1}{3}-\frac{1}{4}$$=\frac{12}{12}=1$
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.

December 8th, 2011, 02:01 PM   #4
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Re: Expectation E(X) Question

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 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.

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 - x²) = 2x² - x³.

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 - x²) = 2x² - x³.
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'.

 December 9th, 2011, 09:04 PM #7 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs Re: Expectation E(X) Question Yes, the following is true: $\int k\cdot f(x)\,dx=k\int f(x)\,dx$ where k is a constant.

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