Sum of binomial random variables

[silentone]

Homework Statement

let y_1 and y_2 be iid bin(5,1/4) random variables

let v=y_1+2*y_2 and u = 3*y_1 -2y_2

find f_uv (u,v) and the cov(u,v)

Homework Equations

f_y (y) = (5 choose y) (1/4)^y (3/4)^5-x for x=0,1,2,3,4,5

covariance=E(uv)-E(u)E(v)

The Attempt at a Solution

By convolution the Sum of bin(n,p) and bin(m,p) = bin (n+m,p)

so pdf of v = bin(15,1/4) and pdf of u = bin (5,1/4)

The only way I know of to get the joint pdf is by a table. Is there a faster way?

 

[haruspex]

For clarity, it's better to use the standard typecase: uppercase for names of r.v.s and lower case for values they take.
When U = u and V = v, what can you say about the values of Y1 and Y2?