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November 3rd, 2015, 04:25 PM   #1
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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)
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November 3rd, 2015, 05:54 PM   #2
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Missing information - probability distributions for X and Y. Also are they assumed independent?
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November 3rd, 2015, 06:04 PM   #3
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Yes, they are assumed independent
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November 4th, 2015, 03:55 PM   #4
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Quote:
Originally Posted by rivaaa View Post
Yes, they are assumed independent
Are the individual distributions uniform?
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November 4th, 2015, 05:30 PM   #5
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Yes, that´s right
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November 5th, 2015, 01:51 PM   #6
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Sums of independent random variables

Above gives general solution. (convolution)
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