5 50 pts Y j 1N are independent random variables with distr

5. (50 pts) Y,, j = 1,...,N are independent random variables with distribution N(mu , sigma^2). Are the following biased or unbiased estimators for p? Find their bias (if any), variance, and MSE. If necessary, express your answers n terms of integrals. a) mu 1 = 1 y ; b) mu 2 = 2 median(Yj) [assume for simplicity that N is odd]; c) mu 3 = 0.5 (Y(1) + Y (N)) 6(75 pts) Yj, j = 1,...,N are independent random variables with distribution U(0, theta). Are the following biased or unbiased estimators for theta? Find their bias (if any), variance, and MSE. Evaluate all integrals. Which has the least MSE and which the most? Does this make sense - why or why not?

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