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(Solved): Problem 1.3. Asymptotic distributions are important for understanding the sampling distributions of ...
Problem 1.3. Asymptotic distributions are important for understanding the sampling distributions of statistics. Answer the followings: (1) Let
{x_(n)}_(n)=1^(\infty )be a sequence of random variables such that each
x_(n)?Bin(n,p_(n))is a binomial random variable with
np_(n)=\lambda for each
n. Show that
x_(n)->dY(where
Y?Poisson(\lambda )in distribution. (2) The sequence of random variables
{x_(n)}_(n)=1^(\infty )is said to
L^(2)-convergent to
x(denoted by (
:x_(n)->t^(2)x