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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)(2xx^2) for 0 <x < 2 0 elsewhere What is the expected value? I got: Integral of x* (3/4)(2xx^2) dx with lower limit is 0 and upper limit is 2. So I rewrote it as: 3/4x (2xx^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 41 =3 I'm confused. My textbook has 1 as the answer for the following problem. But I got a different answer. Help greatly appreciated! 
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: 
December 8th, 2011, 01:25 PM  #3  
Newbie Joined: Oct 2011 Posts: 22 Thanks: 0  Re: Expectation E(X) Question Quote:
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  
Global Moderator Joined: May 2007 Posts: 6,770 Thanks: 700  Re: Expectation E(X) Question Quote:
 
December 8th, 2011, 03:33 PM  #5  
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 Quote:
 
December 9th, 2011, 06:59 PM  #6  
Newbie Joined: Oct 2011 Posts: 22 Thanks: 0  Re: Expectation E(X) Question Quote:
 
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: where k is a constant. 

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