(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Suppose X selects an integer from the set S = {0,1,...,9} and Y selects an integer from {0,...,x^2}. Find:

(a) f(x,y) [joint prob density func]

(b) f_{Y}(y) [marginal for Y]

(c) Probability (Y <= 10 | X = 5)

(d) Probability (Y <= 10 | X <= 5)

2. Relevant equations

3. The attempt at a solution

I'm confused how to start this problem (finding the j.p.d.f.). My teacher's notes are kind of all over the place so this is what I attempted to put together:

(a) f(x,y) = Prob(X=x, Y=y) = f(y|x)f(x)

f(x) = 1/10

f(x,y) = 1/(x^{2}+1) * (1/10)

(b) I'm guessing.. f(y) = Ʃ [ 1/(x^2+1) * (1/10) ]

I'm confused about what the summation is over. In the book it says "probability distribution h(y) of Y alone is obtained by summing f(x,y) over values of X". So does this mean f(y) = Ʃ [ 1/(x^2+1) * (1/10) ] from x=0 to x=9? Or is it from x=y0 (some fixed y) to x=9? If it is the latter case, how do I go about solving this?

Sry, i don't know if I mentioned it but (b) is supposed to be the marginal for Y (and Y alone)

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# Homework Help: Probability density function ?

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