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Math 425 Fall 2024 - HW 10

Due Sunday 11/10, 11:59pm, via Gradescope

Please note:

(1). Please include detailed steps. Only providing the result will not get full credits.

(2). Please write at most one problem in each page. If you reach the bottom please start a new page instead of writing two columns in one page. If a problem contains multiple small questions, you may write them in one page.

(3). Please associate pages with problems in Gradescope.

1. Choose a number X at random from the set of numbers S = {1, 2, 3, 4, 5}.

Now choose a number Y at random from the subset {i ∈ S : i ≤ X}.

(1). Find the joint mass function fX,Y (i, j).

(2). Find the conditional mass function fX|Y (i, j).

(3). Are X and Y independent? Why?

2. The joint p.d.f of X and Y is

Find the conditional p.d.f fX|Y (x, y).

3. If X and Y has joint p.d.f

Compute the joint p.d.f fU,V (u, v), where U = XY and V = X/Y .