Conditional probability distribution.
Let X and Y are the lengths of life, in hours, for two separate electronic component. Their joint density is: f(x; y) = Kexp -(x+y) for x > 0 and y > 0
a) Find the value of k that makes f(x; y) a valid probability distribution.
b) Derive f(x| y)
c) Find P(X < 10| Y = 2)
d) Are X and Y independent? Justify the answer.