c. Let X1, X2, ..., Xn be a random sample from N(0,ơ). Use the Neyman-Pearson lemma to find the best critical region for testing Họ :o² = o3 Ha :o2 = o%, with o > of.
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Part c
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- Let X1,...,Xn be iid random variables with expected value 0, variance 1, and covariance Cov [Xi,Xj] = ρ, for i≠j. Use Theorem of linearity of expectation to find the expected value and variance of the sum Y = X1 +...+Xn.Let X1, ..., Xn be a sample from a geometric random variable with parameter p.(a) Find the maximum likelihood estimator for p.(b) Is the estimator unbiased?(c) Is the estimator consistent?If y1, y2,..., ym be a random sample taken from a normal distribution with parameters x and n× n, then the likelihood equation is
- Suppose that three random variables X1, X2, X3 form a random sample from the uniform distribution on interval [0, 1]. Determine the value of E[(X1-2X2+X3)2]if Y1 and Y2 are independent Poisson random variable with parameters λ1 and λ2 re-spectively. Then find the conditional distribution of Y1 given Y1 + Y2 = n. That is calculateP(Y1 = k|Y1 + Y2 = n).