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1. Let Y, Y, be a random sample of size 2 from the population of Ge-...
Let X1, X2, .. , Xn be a random sample of size n from a geometric distribution with pmf =0.75 . 0.25z-1, f(x) X-1.2.3. ) Let Zn 3 n n-2ућ. Find Mz, (t), the mgf of Žn. Then find the limiting mgf limn→oo MZm (t). What is the limiting distribution of Z,'? Let X1, X2, .. , Xn be a random sample of size n from a geometric distribution with pmf =0.75 . 0.25z-1, f(x) X-1.2.3. ) Let Zn 3...
Question 3 [25] , Yn denote a random sample of size n from a Let Y, Y2, population with an exponential distribution whose density is given by y > 0 if o, otherwise -E70 cumulative distribution function f(y) L ..,Y} denotes the smallest order statistics, show that Y1) = min{Y1, =nYa) 3.1 show that = nY1) is an unbiased estimator for 0. /12/ /13/ 3.2 find the mean square error for MSE(e). 2 f-llays Iat-k)-at 1-P Question 4[25] 4.1 Distinguish...
Let Y,, Y2, .., Yn denote a random sample of size n from a population whose density is given by Find the method of moments estimator for α.
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)
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
Let Zi, Z.Zg be a random sample of size 3 from the N(μ = 0, σ2-1) distribution. Let Xi, X2 be a random sample of size 2 from the N( 1-0,02-2) distribution. Let Y.Y2, Y be a random sample of size 3 from the N(11-1,ơ2-3) distribution. The Xi, Y, and Zi are all mutually independent. Give the distribution (including parameters) of each of the following: 2
A random sample of size 12 is taken from a population, and for each individual in the sample measurements on two variables (X and Y) are obtained. The sample correlation of X and Y is calculated to be r2=0.549081. Carry out a hypothesis test on H0:ρ=0against HA:ρ≠0. If the null hypothesis is true, then the test statistic will follow a t distribution with what degrees of freedom? Number Calculate the value of the test statistic t using the appropriate formula....
QUESTION 7 Let Y, Y2, ....Yn denote a random sample of size n from a population whose density is given by (a) Find an estimator for θ by the maximum likelihood method. (b) Find the maximum likelihood estimator for E( Y4).
QUESTION 7 Let Y,, Y2,..., Yn denote a random sample of size n from a population whose density is given by (a) Find an estimator for 0 by the maximum likelihood method. (b) Find the maximum likelihood estimator for E(Y4).
5.2.1. Let XX be a random sample of size n from the geometric distribution for which p is the probability of success. (a) Use the method of moments to find a point estimator for p. (b) Use the following data (simulated from geometric distribution) to find the moment estimator for p: 2 5743 18 19 16 11 22 4 34 19 21 23 6 21 7 12