My Math Forum Continuous probability; find probability density function

 November 3rd, 2015, 04:25 PM #1 Newbie   Joined: Nov 2015 From: Mexico Posts: 3 Thanks: 0 Continuous probability; find probability density function Let X and Y be random variables and let $Z = \frac{(X+Y)}{2}$. Suppose you randomly choose two numbers X,Y∈[1,3]. Find the probability density function of Z and the expected value E(Z)
 November 3rd, 2015, 05:54 PM #2 Global Moderator   Joined: May 2007 Posts: 6,806 Thanks: 716 Missing information - probability distributions for X and Y. Also are they assumed independent?
 November 3rd, 2015, 06:04 PM #3 Newbie   Joined: Nov 2015 From: Mexico Posts: 3 Thanks: 0 Yes, they are assumed independent
November 4th, 2015, 03:55 PM   #4
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Quote:
 Originally Posted by rivaaa Yes, they are assumed independent
Are the individual distributions uniform?

 November 4th, 2015, 05:30 PM #5 Newbie   Joined: Nov 2015 From: Mexico Posts: 3 Thanks: 0 Yes, that´s right
 November 5th, 2015, 01:51 PM #6 Global Moderator   Joined: May 2007 Posts: 6,806 Thanks: 716 Sums of independent random variables Above gives general solution. (convolution)

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