Let Y 1 2 9 be the order statistics of a random sample of size 9 from the uniform distribution having pdf f(x; θ)=1/θ, 0 5 is an unbiased estimator of θ. Determine the joint pdf of Y 5 and the...

Let Y_1
2
<>₉
be the order statistics of a random sample of size 9 from the uniform distribution having pdf f(x; θ)=1/θ, 0 <><><>₅
is an unbiased estimator of θ. Determine the joint pdf of Y₅
and the sufficient statistic Y₉
for θ. Find the conditional expectation E(2Y₅|y₉) = φ(y₉). Compare the variances of 2Y₅
and φ(Y₉).