Question
Please do by hand. Thanks in advance. 4. Let X1 - uniform(0,3) and X2 – uniform(0,2)...
Please do by hand. Thanks in advance.
4. Let X1 - uniform(0,3) and X2 – uniform(0,2) and suppose that Xi and X2 are independent. Find the pdf of Y1 = X1 + X2. (Hint: First find the joint pdf of Yi and Y2 = X2.)
Answers
Solo when xila, b) - X, ~V (0,3) X2 «U(0,2) - Y=X+X₂ Y2 = X₂ = Xq=Y & X = Y, -Y2 fluta Jointplf of xi$xz ie thugna)= flui) flxz) (asnih are independent) =) flourz) = 3 x 2 fle, 2) = Jointp of of 4,812 flyns ya) = furste) 12 = 42 where I= a d (argaz) alegrage) da dy, da dyz | 10 il J = 1 - flyse) = Marginal pdf of Y=X+Yz ie flyid= = flyn) = 2 / dyz [fly,ayaldyz gas ya=m 23(2-0) fly, a 1/2
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