These are Probability And Statistics Week 9 Assignment 9 Answers
Q1. Let X₁,…, Xm be a random sample from Poisson distribution with parameters λ, 0 < λ. Which of the following is an unbiased estimator of λ? (A) X̅, S² (B) X̅, S², αX̅ + (1 – α)S²; 0 ≤ a ≤1 (C) X̅ (D) S²
Answer: (B) X̅, S², αX̅ + (1 – α)S²; 0 ≤ a ≤1
Q2. Let three random samples of sizes n₁ = 20, n₂ = 10 and n3 = 8 be taken from a population with mean μ and variance σ2. Then which of the following is an unbiased estimator of σ². (A) S²1 (B) S²2 (C) S²3 (D) 20S²1+10S²2+8S²3/38
Answer: (D) 20S²1+10S²2+8S²3/38
These are Probability And Statistics Week 9 Assignment 9 Answers
Q3. Let X₁,…, Xn be a random sample from a gamma population with parameters r and λ. Find the moment estimators of λ and r. (A) X̅, X̅2 (B) 1/X̅, 1/X̅2 (C) X̅/(1/n)Σni=1X2i-X̅2, X̅2/(1/n)Σni=1X2i-X̅2 (D) n-1/X̅, n-1/X̅2
Q4. Let X₁,…, Xn be a random sample from N(0, 1), where θ > 0. Find the MLE of θ. (A) X̅ (B) 1/X̅ (C) X̅² (D) 2X̅
Answer: (A) X̅
These are Probability And Statistics Week 9 Assignment 9 Answers
Q5. Let X₁,…, Xn be a random sample from exponential distribution with mean μ. Find the MSE of an estimator T = 1/n+1Σni=Xi of μ. (A) µ² (B) μ²/n+1 (C) μ²/n(n+1) (D) nμ²/n+1
Answer: (B) μ²/n+1
Q6. Let X be a Bernoulli random variable with P(X = 1) = p and P(X = 0) = 1-p, 0 < p < 1. If μn denotes the nth moment about mean and μ2n+1 = 0 iff (A) p = 1/4 (B) p = 1/3 (C) p = 1/2 (D) p = 2/3
These are Probability And Statistics Week 9 Assignment 9 Answers
Q7. Let X₁,…, Xn be iid random variables with EXi = μ and E|Xi|2 < ∞. Which among the following is a consistent estimator for μ? (A) (Πni=1/Xi)¹/n (B) 2X̅ (C) X(1) (D) 2[n(n+1)]-1Σni=1iXi
Answer: (D) 2[n(n+1)]-1Σni=1iXi
Q8. Let -2,-6,5,9,-5,-9 be the observed values of a random sample of size 6 from population having density function given by fθ(x) = e-(x-θ), x > θ Then MLE of θ is (A) -9 (B) 9 (C) 4/3 (D) -4/3
Answer: (A) -9
These are Probability And Statistics Week 9 Assignment 9 Answers
Q9.
Answer: (C)
Q10. Let X₁,……. Xn be a random sample from U(1,θ) population, where θ > 1. If X(n) = max (X₁, …, Xn), then which of the following is an unbiased estimator of θ ? (A) n+1/n X(n) +1/n (B) n+1/n X(n) -2/n (C) 2X̅ – 1 (D) n/n+1 X(n) + 1/n
Answer: (C) 2X̅ – 1
These are Probability And Statistics Week 9 Assignment 9 Answers
More Weeks of Probability and Statistics: Click Here
