For this question you may assume that linear combinations of normal variates are themselves normally distributed.Let a,b,and c be non-zero constants.
(a)X and Y are independently distributed as N(a,σ2).What is the distribution of (bX+cY)?
(b)If X1,... ,Xn are distributed i.i.d.as N(a, ),what is the distribution of ?
(c)Draw this distribution for different values of n.What is the asymptotic distribution of this statistic?
(d)Comment on the relationship between your diagram and the concept of consistency.
(e)Let = .What is the distribution of ( - a)? Does your answer depend on n?

Question

For this question you may assume that linear combinations of normal variates are themselves normally distributed.Let a,b,and c be non-zero constants.
(a)X and Y are independently distributed as N(a,σ2).What is the distribution of (bX+cY)?
(b)If X1,... ,Xn are distributed i.i.d.as N(a,  ),what is the distribution of   ?
(c)Draw this distribution for different values of n.What is the asymptotic distribution of this statistic?
(d)Comment on the relationship between your diagram and the concept of consistency.
(e)Let  =   .What is the distribution of  (  - a)? Does your answer depend on n?

Quizplus · Accepted Answer

The Answer of For this question you may assume that linear combinations of normal variates are themselves normally distributed.Let a,b,and c be non-zero constants.
(a)X and Y are independently distributed as N(a,σ2).What is the distribution of (bX+cY)?
(b)If X1,... ,Xn are distributed i.i.d.as N(a,  ),what is the distribution of   ?
(c)Draw this distribution for different values of n.What is the asymptotic distribution of this statistic?
(d)Comment on the relationship between your diagram and the concept of consistency.
(e)Let  =   .What is the distribution of  (  - a)? Does your answer depend on n?

For This Question You May Assume That Linear Combinations of Normal