10. A random sample of size n = 15 is drawn from EXP(O). Find c so...
Let X, X,, ..., X, denote a random sample of size n from a population with pdf (10) = b exp(@m()).0<x<1 where (<O<0. Derive that the likelihood ratio test of H.:0=1 versus H, :0 #1 in terms of T(x) = ŽI (3)
A random sample of size n = 2 is taken from the p.d.f f(x) = {1 for 0 ≤ x ≤ 1 and 0 otherwise. Find P(X-bar ≥ 0.9) 3. A random sample of size n = 2 is taken from the p.d.f 1 for 0 < x < 1 f(30 0 otherwise. Find P(X > 0.9)
1. Consider a random sample of size n from a population with pdf: f (x) = (1 -p-p, 0 <p<1, x= 1, 2, ... (a) Show that converges in probability to p. (b) Show that converges in probability to p (1 – p). (c) Find the limiting distribution of
7. (1 point) Let X be the mean of a random sample of size 36 from the uniform distribution U(7,15) Find P(11.3 <X < 11.5)
Problem 5 Let Y1 denote the minimum of a random sample of size n from a distribution that has pdf f(x) e(,0x< o0, zero elsewhere X- n (Y1 0), find the cumulative distribution function (cdf) for Zn = n (Y1 - 0), and Let Zn find the limiting cdf of Zn as n >oo.
[4] (15 pts) Let X1, ... , Xn (n > 2) be a random sample from a Poisson distribution with unknown mean 8 >0. Find the UMVUE of n = P(X1 > 1) = 1 - - (5) (30 pts ; 15 pts each) (a) Let X1,.,X, be a random sample from a Pareto distribution, Pareto(a,1), with pdf f(x; a) = 0x ax-(+1)I(1,00)() where a > 0 is unknown. Find the UMVUE of n = P. (X1 > c) =...
Problem 10: 10 points Assume that a sample {X;:15; <4} of size 4 is drawn from the uniform distribution Unif(-1,1). Consider the maximal order statistic, X(4). 1. Derive density function of X(4) 2. Evaluate expectation of X(4) 3. Determine variance of X(4)
random sample of size n from the p.d.f. 1.8 On the basis of a (x,θ)-θΧθ-1 , 0 < x < 1, θ E Ω = (0,0)derive the MLE of θ
Let X1, X2, ...... Xn be a random sample of size n from EXP() distribution , , zero , elsewhere. Given, mean of distribution and variances and mgf a) Show that the mle for is . Is a consistent estimator for ? b)Show that Fisher information . Is mle of an efficiency estimator for ? why or why not? Justify your answer. c) what is the mle estimator of ? Is the mle of a consistent estimator for ? d) Is...
Problem 3 Let X1, X2, ... , Xn be a random sample of size n from a Gamma distribution fr; a,B) 22-12-1/B, 0 < < (a) Find a sufficient statistics for a. (b) Find a sufficient statistics for B.