compute a 95% upper confidence interval of σ^2 . Q1: Given xi,T2, , and sample second moment is2. Compute the sample variance ,Xn. Suppose n = 10, sample first moment (i.e., sample mean) is s Σία 1x2-2. Compute the sample variance.
Let X = (X1, . . . , Xn) be a random sample of size n with mean μ and variance σ2. Consider Tm i=1 (a) Find the bias of μη(X) for μ. Also find the bias of S2 and ỡXX) for σ2. (b) Show that Hm(X) is consistent. (c) Suppose EIXI < oo. Show that S2 and ỡXX) are consistent. Let X = (X1, . . . , Xn) be a random sample of size n with mean μ...
Let X1 Xn be a random sample of size n from a Bernoulli population with parameter p. Show that p= X is the UMVUE for p. 5.4.22 Let X1 Xn be a random sample of size n from a Bernoulli population with parameter p. Show that p= X is the UMVUE for p. 5.4.22
Given a sample X1,…,Xn∼Uniform(3,10), what sample size ensures that there is a 95% chance that the sample mean is less than 7? a. 457 b. 180 c. 13 d. 256
6. Let X1, . . . , Xn denote a random sample (iid.) of size n from some distribution with unknown μ and σ2-25. Also let X-(1/ . (a) If the sample size n 64, compute the approximate probability that the sample mean X n) Σηι Xi denote the sample mean will be within 0.5 units of the unknown p. (b) If the sample size n must be chosen such that the probability is at least 0.95 that the sample...
1.Suppose X1, X2, .., Xn is a random sample from N(", 02) 10 pts] If o2 1, u is unknown. Find the MLE of a. b. [10 pts If o2 = 1, p is unknown. f = X is an estimator of u. What is the MSE of this estimator? Now assume o2 is unknown. The following data is a set of observations of X1,..., Xn. Use the dataset to answer (c), (d) and (e) 11 8 9 7 6...
Question 3: Bernoulli distribution (23/100 points) Consider a random sample X1,...,Xn from a Bernoulli distribution with unknown parameter p that describes the probability that Xi is equal to 1. That is, Bernoulli(p), i = 1, ..., n. (10) The maximum likelihood (ML) estimator for p is given by ÔML = x (11) n It holds that NPML BIN(n,p). (12) 3.a) (1 point) Give the conservative 100(1 – a)% two-sided equal-tailed confidence interval for p based on ÔML for a given...
1. (50 points) Suppose X1, ..., Xn form a random sample from a N(u,02) distribution with p.d.f. Fe 202, for – V2110 <x< . Assume that o = 2 is known. a) (10 points) Derive the 90% confidence interval for u that has the shortest length. You must show all details including the pivot you use. b) (8 points) Show that the sample mean is an efficient estimator for u. Assume in (c)- (f) that the prior distribution of u...
Let X1, X2, ...,Xn be a random sample of size n from a Poisson distribution with mean 2. Consider a1 = *1782 and în = X. Find RE(21, 22) for n = 25 and interpret the meaning of the RE in the context of this question.
1. Let X1, . . . , Xn be a sample of size n from a distribution with expectation μ (2X1 + X2 + . . . + Xn-1 + 2Xn)/(n+1)l be an estimator and variance σ . and let μ- for μ. Is it unbiased? asymptotically unbiased? consistent?