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December 6th, 2016, 05:17 AM   #1
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How to calculate E(Y), P(X = 1|Y = 2), and E(X|Y = 2)?

Let (X, Y) be a random vector such that
f(y|x) = 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 = 1|Y = 2), and E(X|Y = 2)?
Thanks!
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December 6th, 2016, 06:41 AM   #2
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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$\displaystyle f(y|x)$ 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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