In example 7 13 we found the probability destiny of the
In example 7.13 we found the probability destiny of the sum of two independent random variables having the uniform destiny with α = 0, and β = 1. Given a third random variable X3, which has the same uniform destiny and is independent of both X1 and X2, show that if U = Y + X3 = X1 + X2 + X3, then
(a) The joint probability destiny of U and Y is given by
(b) The probability destiny of U given by
If we let h(1) = h(2) = 1/2, this will make the probability destiny of U continues.
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