Hint: Use characteristic function. (I guess the convergence is in distribution)
Wn has density [1+(x/n)]/[1+(0.5n)] for 0<x<1, and 0 otherwise. The random variable W has a uniform distribution on [0,1]. Prove that {Wn} converges in distribution to W.
i have so far that
FWn(w) = 0 for all w
Fw(w)=0 if w<=0, w if 0<w<1, 1 if w>=1
How do I show the convergence?
Hint: Use characteristic function. (I guess the convergence is in distribution)
In the long run, we're all dead.
I have no idea how to use it...
I'm guessing the moment generating function works in this situation? Anywho, show that the MGFs converge and then use the fact that MGFs are unique.
ok so this is what i get
mWn(s)=E(e^(sWn))= integral (0 to 1): e^(sWn)*((1+(x/n)))/(1+(1/2n))dWn
which equals (as lim n-> inf.)
integral (0 to 1): e^(Sw)dw
mW(s)=E(e^(Sw))=integral (0 to 1): e^(Sw)dw
is this right so far?
Last edited by omega; 11-20-2010 at 03:08 PM.
Tweet |