X 1 2

0.5 0.5

p(Y & lt； = y | x = 1)= 1-e(- Jin 1y)

p(Y & lt； = y | x = 2)= 1-e(- into 2y)

p(Y & lt； = Y)= P(X = 1)P(Y & lt； = Y | X = 1)+P(X = 2)P(Y & lt； =y| X=2)

= 1-{ e(- in 1y)+e(- in 2y)}/2

2

For p (y

Fy(y)={ input1e (input 1y)+ 2e (input 2y)}/2

three

P(X= 1| By)

= P(X = 1 | Y & lt； =2)

=P(X= 1，Y & lt= 2)/P(Y & lt； =2)

P(X= 1，Y & lt= y) = ( 1-e (- 1y)/2

P(X= 1, Y<= 2) = (1-E (-2 1))/2.

p(Y & lt； = 2) = 1-{E (-2 into 1)+E (-2 into 2)}/2

P(X= 1，Y & lt= 2)/P(Y & lt； =2)

= {1-E (-2 in1)} {2-e (-2 in 1)-E (-2 in 2)}