b) Draw and integrate
d) Find f(y|x) and integrate.
1) Assume that (X,Y) has the following density function
f(x,y) = 2e^-(x+y) when 0 < x < y
a) Find the marginal density function fx(x) and fy(y)
b) Find the probability that P (Y < 2X)
c) Find P(Y < 1 given X < 1)
d) Find P(Y < 1 given X = 1/2). Also the E(Y given X=1/2).
For b), what do I draw?
For c), isnt it P(A union B)/ P(B)? And how do I know what something like P(B) is? Integrate from 0 to 1 with X? Not exactly sure what to ask, but I'm still confused.
And for d), for the expectation part, do I just integrate with y * f(Y given x)?