according to Basu's theorem V and xbar/ s are independent
Let X1, ..., Xn be a random sample from a distribution with pdf 2πσχ (a) If σ and μ are both unkn...
6. Suppose that X1,X2 , Xn form a random sample from a normal distribution N(μ, σ 2), both unknown. consider the hypotheses Construct a likelihood ratio test and show that this LRT is equivalent to a t-test 6. Suppose that X1,X2 , Xn form a random sample from a normal distribution N(μ, σ 2), both unknown. consider the hypotheses Construct a likelihood ratio test and show that this LRT is equivalent to a t-test
Let Xi, , Xn be a random sample from a n(o, σ*) distribution with pdf given by 2πσ I. Is the distribution family {f(x; σ), σ 0} complete? 2. Is PCH)〈1) the same for all σ ? 3. Find a sufficient statistic for σ. 4. Is the sufficient statistic from (c) also complete!? Let Xi, , Xn be a random sample from a n(o, σ*) distribution with pdf given by 2πσ I. Is the distribution family {f(x; σ), σ 0}...
Problem 3. Consider a random sample X1, X2,..., Xn from a distribution with log-normal pdf (density function): for t 0 and 0 otherwise. Both μ and σ 0 are unknown parameters. Find the method of moments estinates μ and σ. Hint: computing moments, change of variable y = Int might be useful.
Problem 3. Consider a random sample X1, X2,..., Xn from a distribution with log-normal pdf (density function): for t 0 and 0 otherwise. Both μ and σ 0 are unknown parameters. Find the method of moments estinates μ and σ. Hint: computing moments, change of variable y = Int might be useful.
Let X1,X2, , Xn be a random sample from a normal distribution with a known mean μ (xi-A)2 and variance σ unknown. Let ơ-- Show that a (1-α) 100% confidence interval for σ2 is (nơ2/X2/2,n, nơ2A-a/2,n). Let X1,X2, , Xn be a random sample from a normal distribution with a known mean μ (xi-A)2 and variance σ unknown. Let ơ-- Show that a (1-α) 100% confidence interval for σ2 is (nơ2/X2/2,n, nơ2A-a/2,n).
1. Let X1, ..., Xn be a random sample from a distribution with cumulative dist: 10, <<0 F(x) = (/), 0<x<B | 1, >B > (a) For this part, assume that is known and B is unknown. Find the method of moments estimator Boom of B. (b) For this part, assume that both 6 and B are unknown. Find the maximum likelihood estimators of 8 and B.
Let X1, X2, . . . , Xn be a random sample from some distribution and suppose Y = T(X1, X2, . . . , Xn) is a statistic. Suppose the sampling distribution of Y has PDF fY (y) = 3 8 y 2 for 0 ≤ y ≤ 2. Find P[0 ≤ Y ≤ 1 5 ].
QUESTION 2 Let Xi.. Xn be a random sample from a N (μ, σ 2) distribution, and let S2 and Š-n--S2 be two estimators of σ2. Given: E (S2) σ 2 and V (S2) - ya-X)2 n-l -σ (a) Determine: E S2): (l) V (S2); and (il) MSE (S) (b) Which of s2 and S2 has a larger mean square error? (c) Suppose thatnis an estimator of e based on a random sample of size n. Another equivalent definition of...
Let X1, . . . , Xn be a random sample from a population with density 8. Let Xi,... ,Xn be a random sample from a population with density 17 J 2.rg2 , if 0<、〈릉 0 , if otherwise ( a) Find the maximum likelihood estimator (MLE) of θ . (b) Find a sufficient statistic for θ (c) Is the above MLE a minimal sufficient statistic? Explain fully.
Let X1, . . . , Xn be a random sample from the uniform distribution on the interval (θ, θ + 1), θ > 0. Find a sufficient statistic for θ.