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 .