5. Suppose we observe Y Yn from a normal distribution with unknown parameters such that '...
5. Suppose we obaerve Y. ..Y, from a normal distribution with unknown parameters such that P - 20, s n=10. 16, and (a) Find a 95% confidence interval for (b) Now suppose n-1000, with the same value of Y and s. Find a 95% confidence interval for G) Would your answer to (a) or (b) change if the data were not from a normal distribution?
6. Suppose we observe Y,... Yn from a normal distribution with unknown parameters such that Y 24, s2 36, and n 15. (a) Find the rejection region of a level α-0.05 test of H0 : μ-20 vs. H1 : μ * 20. Would this test reject with the given data? (b) Find the rejection region of a level α -0.05 test of Ho : μ < 20 vs. H1 : μ > 20 would this test reject with the given...
6. Suppose we obeerve Yi,...Yn from a normal distribution with unknown parameters such that Y 24, 236, and (a) Find the rejection region of a level a-0.05 test of Ho : μ-20 vs. Hi :"t 20. Would this test reject with the (b) Find the rejection region of a level α-0.05 test of Ho : μ 20 vs. H: μ > 20, would this test reject with the given data? given data? (c) Will the p-value for the given data...
3. Suppose that the random variable X is an observation from a normal distribution with unknown mean μ and variance σ (a) 95% confidence interval for μ. (b) 95% upper confidence limit for μ. (c) 95% lower confidence limit for μ. 1 . Find a
8.40 stion 4 (6 pt) (Ex. 8.40 on page 409 is modified): Suppose that random variable Y is an observation from a normal distribution with unknown mean u and variance l Find and verify a pivotal quantity that you can use to derive confidence limits for the mean u. Find a 95% lower confidence limit for. a. b. 8.40 Suppose that the random variable Yis an observation from a normal distribution with unknown mean μ and variance 1 . Find...
6 and 7 6. Suppose we observe Y...Yn from a normal distribution with alaiuctess n 15 (a) Find the rejection region of a level a 0.05 test of Ho 20 vs. H20. Would this test reject with the given data? (b) Find the rejection region of a level a-0.05 test of H0 : 20 vs. Hi : > 20. Would this test reject with the given data? (c) Will the p-value for the given data be smaller in part (a)...
Could I grab some help on problem 2? Thank you 2. Suppose Yi, Yn are iid normal random variables with normal distribution with unknown mean and variance, μ and ơ2. Let Y ni Y. For this problem you may not assume that n is large. n (a) What is the distribution of Y? (b) What is the distribution of Z = (yo)' + ( μ)' + (⅓ュ)? (o) What is the distribution of ta yis (d) What is the distribution...
4 and 5 samples, the other in small samples. Which is which? Explain. (d) Suppose we know that the 5 values are from a symmetric distribution. Then the sample median is also unbiased and consistent for the population mean. The sample mean has lower variance. Would you prefer to use the sample 4. Suppose Yi, Y, are iid r ables with E(n)-μ, Var(K)-σ2 < oo. For large n, find the approximate 5. Suppose we observe Yi...Yn from a normal distribution...
Y1, Y2, ... Yn are a random sample from the Gamma distribution with parameters α and β (a) Suppose that α-4 is known and β is unknown. Find a complete sufficient statistic for β. Find the MVUE of β. (Hint: What is E(Y)?) (b) Suppose that β = 4 is known and a is unknown. Find a complete sufficient statistic for α.
Bayesian updating Suppose that we have the model y|μ ~ N(μ, τ-1) where τ > 0 is known and μ is an unknown parameter (vi) Suppose that ( of y with a -ab1. Suppose that you observe a realization Compute the posterior distribution value of 1. π(μ|1) and explain how it relates to π(μ). vii) Suppose now that you observe a second realization of y with a value of -1. Update the posterior π(p11) to incorporate this new information. Bayesian...