STAT 330: 98_1
Assignment 4 Solutions
This is equal to when or . In this case and we get .
The derivative of this with respect to is which is 0 when which gives the estimate ?. (I haven't worked it out yet.)
The derivative of this with respect to y is the density of Y so the density is which is part a).
which is not . Thus Y is biased but so that is unbiased.
which is a minimum when is minimized. Take the derivative with respect to K and set it equal to 0 to get 4K/(n-1)+2K = 2 whose solution is K=(n-1)/(n+1).
The derivative with respect to is simply which is 0 when . Put this in for each and note that
Now take the derivative with respect to to get
which is 0 when