please finish the questions without any programming.

3)LetX, Y be two continuous random variables with joint density function

8 xy / q 4if0 < y < x< q

f(x,yÂ½q)=

otherwise .

We want to estimate q relative to Mean Square Error (MSE).From lecture we already know that X is a sufficient statistic forq and has density function

fX (xÂ½q)=4 x3 / q4 if0 < x < q

0 otherwise

Consider the estimatord (x,y) =3 x y. Without computing any MSE find an estimator that will have smaller MSE than the estimatord (x,y)=3 x y and explain why that should be true.

4)We have one observation,Y,having pdf, for -1â‰¤qâ‰¤1, equal to

2 y q + 1if-1/2<y<1/2

f (yÂ½q)=

0otherwise.

NOTE:For f (yÂ½q) to be a density function the only possible values ofq must be in the closed interval -1â‰¤ qâ‰¤1.

Consider the estimator W(y) defined as

W( y)= 1ifyÂ³0

-1ify <0

a.IsW(y)an unbiased estimator ofq?

b..Show that W(y) is an MLEofq.

Do you need a similar assignment done for you from scratch? We have qualified writers to help you. We assure you an A+ quality paper that is free from plagiarism. Order now for an Amazing Discount! Use Discount Code “Newclient” for a 15% Discount!NB: We do not resell papers. Upon ordering, we do an original paper exclusively for you.

The post intro theory of statistics 1 appeared first on My Nursing Experts.