1 point Suppose that random variables X1 and X2 have the fol

(1 point) Suppose that random variables X1 and X2 have the following joint density function. Use the distribution function technique to find the probability density of Y = X1 + X2.

Solution

f(x1,x2) = intrigrate 1/152 (3x1+x2)dx1dx2 = x1>0 , x2 > 0 , x1+ 6x2 < 12 means

x1= 1 ,2, 3, 4 ,5 x2 = 1

f(x1,x2) = 1/304(304c1x+3x^2y+xy^2)+c2 y = x1 + x2 2<= y < = 6

f(x1) = 1/152(3x1^2/2+x1x2) + c x1> 0 x1< 5 y x2 = 1

f(x2) = 1/152 (3x1x2+ y^2/2) x1> 0 x1< 5 y x2 = 1

Y = X1+ X2 1< y < = 6

0 else where