9. Let X₁, X2,..., Xn be the random sample from a normal distribution with mean and variance o². Let X = ²/1 X₁ and S² = ¹₁ Σ²-1(X; - X)² be the sample mean and sample variance, respectively. n-1 n (a). Find the maximum likelihood estimate (MLE) of (u,0²) (b). Find the method of moments estimators (MME) of (μ, o²) (c). Derive the E(X), Var(X), and the distribution of sample mean X.
9. Let X₁, X2,..., Xn be the random sample from a normal distribution with mean and variance o². Let X = ²/1 X₁ and S² = ¹₁ Σ²-1(X; - X)² be the sample mean and sample variance, respectively. n-1 n (a). Find the maximum likelihood estimate (MLE) of (u,0²) (b). Find the method of moments estimators (MME) of (μ, o²) (c). Derive the E(X), Var(X), and the distribution of sample mean X.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Question

Transcribed Image Text:9. Let X₁, X2,..., Xn be the random sample from a normal distribution with mean and variance o². Let
X = 1/1 X₁ and S² = ¹₁-1(X₁ - X)² be the sample mean and sample variance, respectively.
(a). Find the maximum likelihood estimate (MLE) of (μ, 0²)
(b). Find the method of moments estimators (MME) of (μ,0²)
(c). Derive the E(X), Var(X), and the distribution of sample mean X.
(d). Find the E(S2). Is S22 an unbiased estimator of o²?
(e). Write the distribution of (n-1)²
(f). State the distribution of (X). Explain it briefly.
Sn/√n
(g). Find the (1-a) 100% confidence interval for μ.
(h). Find the approximate (1-a) 100% confidence interval for u.
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