I have a couple of exercise questions i'm having trouble with which any help would be much appreciated.
1. Suppose N is exponentially distributed with parameter lambda. Given N, the R.V X has uniform distribution in the interval [0,N]. Evaluate E(X) and Var(X).
I tried using E(X)=E[E(X|N)] and worked from their but confused myself...
2.Suppose X and Y are independent standard normal variables. Let S=X+2Y and T=X-2Y.
a)Evaluate Cov(S,T) and Cov(S-T,2S+T)
b)Show that (S,T) has bivariate normal distribution
For a), I worked out:
=Cov(4Y,2Y)=I dont know
b)I have no idea...
Thanks in advance.