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December 6th, 2016, 05:17 AM  #1 
Newbie Joined: Dec 2016 From: Canada Posts: 1 Thanks: 0  How to calculate E(Y), P(X = 1Y = 2), and E(XY = 2)?
Let (X, Y) be a random vector such that f(yx) = 1/x if y = 1, 2, . . . ,x ..........= 0 elsewhere. (For any positive integer x). Also let X has the following p.m.f. f(x) = 1/3 if x = 1, 2, 3 ......= 0 elsewhere. How to calculate E(Y), P(X = 1Y = 2), and E(XY = 2)? Thanks! 
December 6th, 2016, 06:41 AM  #2 
Senior Member Joined: Apr 2014 From: Glasgow Posts: 1,842 Thanks: 593 Math Focus: Physics, mathematical modelling, numerical and computational solutions  http://aix1.uottawa.ca/~zarepour/mat2371/a5.pdf Nice try Here's some hints: 1. The random vector$\displaystyle f(yx)$ is a harmonic series when x = infinity, but it is finite if x is finite and can be normalised to form a p.m.f. if x is known. 2. What values can x be? 3. $\displaystyle E(Y) = \sum y P(y)$ 

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