This preview shows page 1. Sign up to view the full content.
Unformatted text preview: this to the bound you get from Chebyshevs inequality. 3. Consider the sequence of independent random variables X 1 , X 2 , . . . where X n bin ( n, p ). For i = 1 , 2 , . . . , dene Y n = X n /n . Investigate the convergence in probability of Y n . (i.e.: Say what it converges to and show it!) 4. Let X 1 , X 2 , . . . , X n be a random sample from the distribution with pdf f ( x ) = 1 x 2 I (1 , ) ( x ) . (a) Find the limiting distribution of X (1) = min( X 1 , X 2 , . . . , X n ). (b) Find the limiting distribution of n ln X (1) . 5. Let X ( n ) = max( X 1 , X 2 , . . . , X n ) where X 1 , X 2 , . . . , X n is a random sample from any contin-uous distribution that has cdf F ( x ) and pdf f ( x ). Dene Z n = n [1-F ( X ( n ) )]. Find the limiting distribution (convergence in distribution) of Z n ....
View Full Document
This note was uploaded on 02/07/2012 for the course APPM 4520 taught by Professor Manuel during the Fall '11 term at University of Colorado Denver.
- Fall '11