Let X1,...,Xn ∼ iid N(μ,τ) with both μ and τ unknown. Consider estimators of the form δb(x) = bS2, where S2 = ∑ni=1(Xi −X ̄)2. Note that we have already considered estimators of this form with b = 1/n and b = 1/n−1. (a) Calculate the MSE for δb(x) as a function of the choice b. (b) Find the value of b (depending on n) that minimizes the MSE. (c) Is the resulting estimator unbiased? If not, what is the bias?

Q: Consider the following. x2 z = x3 + 1 - x - 4x2 Let u(x) = x² and v(x) = 1 – x – 4x2. %3D %3D Find…

A:

Q: 1. Find the derivative of the following functions: a. y = x² b. y=x4 c. y=- X

A:

Q: Let h(x) = f(g(x)) and p(x) = g(f(x)). Use the table below to compute the following derivatives. a.…

A: h(x)=fgx and px=gfx

Q: 5. Evaluate (x) dx for the following functions: 1 (a) f(x) = Vx + (b) f(x) = e2x %3D (c) f(x) =…

A:

Q: Consider the function f(x) = eª sin(3x). 1. Compute the exact derivative f'(x) using analytical…

A:

Q: 3. Find the derivative. sh (a)l= - पक) (a) f(x) = x2 cos x +x tan r (b) h(x) = e" (x² + 4x) %3D t2…

A:

Q: Exercise 2.6 Find derivatives of the following functions: i. y = ln(x²+2x+3) iii. f (t) = 1 e2t ==…

A: Step 1: For y=ln(x2+2x+3): Identify the function: y=ln(u), where u=x2+2x+3. Apply the chain rule:…

Q: Letr = (e141-11, e9-9¹, (t + 1)−6). Compute the derivative. (Use symbolic notation and fractions…

A:

Q: Find the second derivative of the following functions: a. f(x) = x5 + sin x b. f(x) = x² + == x c.…

A:

Q: 1. The derivative of the function I (x) which is given by f )=-2x+3 atx4is A. 59 B. 48 C. 46 D. 10 E…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 4. Find the following derivatives. (1) Suppose that y=sin(xcos x), find y (2) Find the first and…

A: Find the derivatives