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.

Transcribed Image Text:

for Regions I and II of Figure 7.9 for Regions 11 I and IV of Figure 7.9 elsewhere y g(uゾ)=12-y 0 for u s0 for 0u1 for 1 <<2 0 u2 tA 万112-5W-1)2+5(11-2)2 for 2 < 11 <3 Tor WE3