P(Yn=k)= ( (1-2^(-n-1))^(-1) )/ 2^(k+1) for k=0,1,2,...,n. The random variable Y has the geometric distribution where lambda is 1/2. How can I prove that {Yn} converges in distribution to Y?
Any help is appriciated.
I get fY(y)=1/2^(y+1)
but how do I prove the convergence?
i'm a bit confused here, in your Fyn(y), for the equation where 0<=y<n, why did you put x(1-y) and not 1-(xy)? (x and y represents the parts of Yn)
Also in your Fyn(y), what about 1 if y>=1 since its a cdf ? if you don't add that part, doesn't it make it 1 if y>=0 ?
Last edited by omega; 11-19-2010 at 11:40 PM.
Tweet |