convergence problem on random variables

• Nov 21st 2010, 09:03 AM
Sneaky
convergence problem on random variables
Suppose P(Yn<=y)=1-e^(-2ny/(n+1)) for all y>0. Prove that Yn converges in distribution to Y where Y has the exponential distribution for some lambda >0 and compute lambda.

so for this i get
[lim n->inf] 1-e^(-(2ny)/(n+1)) -> 1-e^(-y*lambda)

I'm not sure how to prove the convergence here...
Is it enough to say that lambda = (2n)/(n+1) ?
since 2n > n+1, the result will always be > 1, which is what lambda can be.
• Nov 21st 2010, 03:16 PM
Focus
What is the limit of $\frac{n}{n+1}$? Why is $\lim e^{x_n}=e^{\lim x_n}$?
• Nov 21st 2010, 03:31 PM
Sneaky
nvm i figured it out, lambda = 2