Let X1, , Xn be a random sample from a n(0, 2X), and let Y1, , Ym be a random sample from a n(0, 2Y), independent of the As Define 2Y 2X a Find the level a LRT of H0 0 versus H1 0 b Express the rejection region of the LRT of part (a) in terms of an F random variable c Find a 1 confidence interval f...

a The unrestricted MLEs of 2 X and 2 Y are 2 X X 2 i n and 2 Y Y 2 i m as usual Under the restrictio ...

Let X1,..., Xn be a random sample from a n(0, 2X), and let Y1,..., Ym be a

Question:

Let X1,..., Xn be a random sample from a n(0, σ2X), and let Y1,..., Ym be a random sample from a n(0, σ2Y), independent of the As. Define λ = σ2Y/ σ2X.
a. Find the level a LRT of H0: λ = λ0 versus H1: λ ≠ λ0.
b. Express the rejection region of the LRT of part (a) in terms of an F random variable.
c. Find a 1 - α confidence interval for λ.