3) [10 points Let yi, yz, , a ncel Finyt be a random sample from a normal distribution with unknown mean μ Ho: μ-μο against H, : μ-μι. 3) [10 points Let yi, yz, , a ncel Finyt be a random...
8) Let Yi, X, denote a random sample from a normal distribution with mean μ and variance σ , with known μ and unknown σ' . You are given that Σ(X-μ)2 is sufficient for σ a) Find El Σ(X-μ). |. Show all steps. Use the fact that: Var(Y)-E(P)-(BY)' i-1 b) Find the MVUE of σ.
QUESTION 6 1 points s Consider the hypothesis test Ho μι-μ2 against H, μι-μ 2 . Suppose that sample sizes are n1-15 and n2-15 and X, 4.5 and X2 -8.0 and that s-4 and s-6.18. Assume that the data are drawn from normal distributions. Compute the p-value of the test statistics. Round your answer to 4 decimal places
QUESTION: Yi, Y2, Y, denote a random sample from the normal distribution with known mean μ 0 and unknown variance σ 2, find t 1 he method-of-moments estimator of σ 2 C2. Continue with Exercise 9.71. Find the MLE of σ2.
2. Suppose Yi,.. narei normal random variables with normal distribution with unknown mean and variance, μ and or. Let Y-욤 Σ;..x. For this problem, you may not assume that n is large. (a) What is the distribution of Y? (b) what is the distribution of z-(yo), (en, (n-) (c) what is the distribution of (n-p? (d) What is the distribution of Justify your answer. (e) Let Zi-(ga)' + (-)' + (yo)", z2 = (속)' + (n-e)' what is the distribution...
Let Yi, Ys,.., Y's be a random sample of size 5 from a normal distribution mean 0 and standard deviation 1 and let-3x /5 . Let Y6 be another independent observation from the same distribution. Find the distributions of the following random variables i-1 2(572 +Y) (b) WW Let Yi, Ys,.., Y's be a random sample of size 5 from a normal distribution mean 0 and standard deviation 1 and let-3x /5 . Let Y6 be another independent observation from...
FR2 (4+4+4 12 points) (a) Let XI, X2, X10 be a randoin sample from N(μι,σ?) and Yi, Y2, 10 , Y 15 be a random sample from N (μ2, σ2), where all parameters are unknown. Sup- pose Σ 1 (Xi X 2 0 321 (Y-Y )2-100. obtain a 99% confidence interval for σ of having the form b, 0o) for some number b (No derivation needed). (b) 60 random points are selected from the unit interval (r:0 . We want...
Problem3 (15 points (a) (8 points) Let x, X, be a random sample from normal distribution NG, σ, . s are sample mean and sample variance. Consider the probabilities PC, μ) and PS? σ)-are they equal? (b) (7 points) Let X, , ,X, be a random sample from normal distribution Mo, σ, R, s are sample mean and sample variance. Let y.... is and independent sample from the same distribution. Y, s are corresponding sample mean and sample variance. Let...
please answer with full soultion. with explantion. (4 points) Let Xi, , Xn denote a randon sample from a Normal N(μ, 1) distribution, with 11 as the unknown parameter. Let X denote the sample mean. (Note that the mean and the variance of a normal N(μ, σ2) distribution is μ and σ2, respectively.) Is X2 an unbiased estimator for 112? Explain your answer. (Hint: Recall the fornula E(X2) (E(X)Var(X) and apply this formula for X - be careful on the...
A sample of 27 independent observations is taken from a normal distribution of unknown mean μ but known variance σ. 75.24. The sample mean is 5 is the width of the 98% confidence interval for μ? 4.42 and the sample variance is 41. What A sample of 27 independent observations is taken from a normal distribution of unknown mean μ but known variance σ. 75.24. The sample mean is 5 is the width of the 98% confidence interval for μ?...
Yi, Y2...., Yn is a random sample from the Uniform distribution ([a, b]). Let u to be the population mean, one wants to test Ho : μ = 1 against Ha : μ 1. Suppose n is large, and both the one-sample t-test and the binomial test can be applied here. Derive the approximate analytic formula for computing the power for each of the test. Besides the sample size n and significance level α, what quantity is essential in the...