Question

Let Y_(1),Y_(2),Y_(3),Y_(4),Y_(5) be an independent and identically distributed sample of size 5 from a normal population with mean 0 and variance 1 and let /bar (Y)=((1)/(5))sum_(i=1)^5 Y_(i). Let Y_(6) be another independent observation from the same population. (a) What is the distribution of W=sum_(i=1)^5 Y_(i)^(2) ? (b) What is the distribution of U=sum_(i=1)^5 (Y_(i)-(/bar (Y)))^(2) ? (c) What is the distribution of sum_(i=1)^5 (Y_(i)-(/bar (Y)))^(2)+Y_(6)^(2) ? (d) What is the distribution of sqrt(5)(Y_(6))/(sqrt(W)), where W is defined in part (a)? (e) What is the distribution of 2(Y_(6))/(sqrt(U)), where U is defined in part (b)? (f) What is the distribution of 2((5)/(b)ar (Y)^(2)+Y_(6)^(2))/(U), where U is defined in part (b)?

          Let Y_(1),Y_(2),Y_(3),Y_(4),Y_(5) be an independent and identically distributed sample of size 5 from a
normal population with mean 0 and variance 1 and let /bar (Y)=((1)/(5))sum_(i=1)^5 Y_(i). Let Y_(6) be another
independent observation from the same population.
(a) What is the distribution of W=sum_(i=1)^5 Y_(i)^(2) ?
(b) What is the distribution of U=sum_(i=1)^5 (Y_(i)-(/bar (Y)))^(2) ?
(c) What is the distribution of sum_(i=1)^5 (Y_(i)-(/bar (Y)))^(2)+Y_(6)^(2) ?
(d) What is the distribution of sqrt(5)(Y_(6))/(sqrt(W)), where W is defined in part (a)?
(e) What is the distribution of 2(Y_(6))/(sqrt(U)), where U is defined in part (b)?
(f) What is the distribution of 2((5)/(b)ar (Y)^(2)+Y_(6)^(2))/(U), where U is defined in part (b)?

Added by Kathleen Y.

Question

Please give Ace some feedback