Let Y1,K,Y n denote a random sample from a Poisson distribution with parameter λ .
a. Find a sufficient statistics for λ.
b. Find the minimum variance unbiased estimator(MVUE) of λ2 .
Let Y1,K,Y n denote a random sample from a Poisson distribution with parameter λ . a....
7.41. Let X. X. ..., X, denote a random sample from a distribution that is N(0, 0). Then Y- X is a complete sufficient statistic for 0. Find the unbiased minimum variance estimator of .
need the solution for this question.tq Let X,,. X, be a random sample from a Poisson (a) (a). 2. distribution. Find the sufficient statistic for A. (25 marks) Let X,X,X, be a random sample from a gamma (k, B) (b). P.1 distribution with k is fixed. DefineX X, n피 based upon unbiased ness, consistency Evaluate (0). and efficiency is a minimum variance unbiased estimator for B Show that (ii). (75 marks) (2)3 Let X,,. X, be a random sample from...
Suppose that Y1 , Y2 ,..., Yn denote a random sample of size n from a normal population with mean μ and variance 2 . Problem # 2: Suppose that Y , Y,,...,Y, denote a random sample of size n from a normal population with mean u and variance o . Then it can be shown that (n-1)S2 p_has a chi-square distribution with (n-1) degrees of freedom. o2 a. Show that S2 is an unbiased estimator of o. b....
7. Let X1,....Xn random sample from a Bernoulli distribution with parameter p. A random variable X with Bernoulli distribution has a probability mass function (pmf) of with E(X) = p and Var(X) = p(1-p). (a) Find the method of moments (MOM) estimator of p. (b) Find a sufficient statistic for p. (Hint: Be careful when you write the joint pmf. Don't forget to sum the whole power of each term, that is, for the second term you will have (1...
POINT ESTIMATION Let be a simple random sample of a population with Poisson distribution , . Find the MVUE ( minimum-variance unbiased estimator ) for and for Thank you for your explanations X1, X2,..,X n P(0) We were unable to transcribe this imaged (0 d (0)P (X=0 X1, X2,..,X n P(0) d (0 d (0)P (X=0
10. Let Y1,..., Y, be a random sample from a distribution with pdf 0<y< elsewhere f(x) = { $(0 –» a) Find E(Y). b) Find the method of moments estimator for 8. c) Let X be an estimator of 8. Is it an unbiased estimator? Find the mean square error of X. Show work
Let X1,X2,,X be a random sample from a distribution function f(x,8) = θ"(1-8)1-r for x = 0,1 (a) Show that Y = Σ.1X, is a sufficient statistic for θ. (i) Find a function of Y that is an unbiased estimate for θ (ii) Hence, explain why this function is the minimum variance unbiased estimator(MVUE) for θ (c) Is1-the MVUE for Please explain.
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.
(a)Suppose X ∼ Poisson(λ) and Y ∼ Poisson(γ) are independent, prove that X + Y ∼ Poisson(λ + γ). (b)Let X1, . . . , Xn be an iid random sample from Poisson(λ), provide a sufficient statistic for λ and justify your answer. (c)Under the setting of part (b), show λb = 1 n Pn i=1 Xi is consistent estimator of λ. (d)Use the Central Limit Theorem to find an asymptotic normal distribution for λb defined in part (c), justify...
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...