If X and Y are independent and identically distributed uniform random variables on (0,1) compute the joint density of
U = X+Y, V = X/(X+Y)
Part A,
The state space of (U,V) i.e. the domain D over which fU,Y (u,v) is non-zero can be expressed as
(D = {(u,v) R x R] 0 < h1(u,v) < 1, 0 < h2(u,v) < 1} where x = h1 (u,v) and y = h2 (u,v)
Find h1(u,v) = (write a function in terms of u and v)
Find h2(1,0.25)
Part B,
For (u,v) D, fU,V(u,v) = (answer)
uv = x
h1(u,v) = uv
y = U - x = U - UV = U(1-V)
hence
h2(u,v) = U(1-V)
If X and Y are independent and identically distributed uniform random variables on (0,1) compute the...
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