question: B1. A random sample of n observations, Yi, ..., Yn, is selected from a pop-...
B1. A random sample of n observations, Yi, ., Yn, is selected from a pop- ulation in which Yi, for i = 1, 2, ,n, possesses a common distribution the same as that of the population distribution Y (a) Suppose that we know Y has a Geometric distribution with parameter p, p unknown. Find the estimator using the method of moments. (b) Suppose that we know that Y has an exponential distribution with parameter λ, λ unknown. Find the estimator...
previously, the problem b1(a) is Suppose that we know Y has a
Geometric distribution with parameter p, p unknown. Find the
estimator p using the method of moments.
BUT, in this problem, THE QUESTION IS: FIND THE MLE OF P.
B1. A random sample of n observations, Yi, ..., Yn, is selected from a pop ulation in which Yi, for 1,2,..., n, possesses a common distribution the same as that of the population distribution Y. C3. Continue with Problem B1...
Al. A random sample of n observations, Yi, ..., Yn, is selected from a pop- ulation in which Yi, for i-1, 2, ..., n, possesses a common distribution the same as that of the population distribution Y. (a) Suppose that Y has a Binomial distribution B(N, P). If N is known, P is unknown, find out the estimator P using the method of moments (b) If N and P are both unknown, find out the estimators P and N using...
1. Suppose Yi, ½ . . . , Yn is a random sample of n independent observations from a distribution with pdf 202 fY()otherwise. (a) Find the MLE for θ (c) Use the pivotal quantity to find a 100(1-a)% CI for θ
1. Suppose Yi, ½ . . . , Yn is a random sample of n independent observations from a distribution with pdf 202 fY()otherwise. (a) Find the MLE for θ (c) Use the pivotal quantity to find a...
QUESTION:
Yi, Y2, Y, denote a random sample from the normal distribution with known mean μ 0 and unknown variance σ 2, find t 1 he method-of-moments estimator of σ 2 C2. Continue with Exercise 9.71. Find the MLE of σ2.
1. Suppose Yi,½, , Yn is an iid sample from a Bernoulli(p) population distribution, where 0< p<1 is unknown. The population pmf is py(ulp) otherwise 0, (a) Prove that Y is the maximum likelihood estimator of p. (b) Find the maximum likelihood estimator of T(p)-loglp/(1 - p)], the log-odds of p.
1. Suppose Yi,½, , Yn is an iid sample from a Bernoulli(p) population distribution, where 0
4. Let Yi, ½, . . . , Yn be a random sample from some pdf/pmf f(y; θ)·Let W be a point estimator h(y, Y2, . . . , Yn) for θ. The bias of W as a point estimator for θ is defined as W Blase(W) = E(W)- The mean square error of W is defined as MSEe(W) = E(W-0)2 (a) Using properties of expected values, and the definition of variance from PSTAT 120A/B, show that MSEe(W) = Vare(W)...
QUESTION 5 Let Y , Y2, , Yn denote a random sample of size n from a population whose density is given by (a) Find the method of moments estimator for β given that α is known. Find the mean and variance of p (b) (c) show that β is a consistent estimator for β.
7. (12 points) Let Yı,Y2, ..., Yn be a random sample from Gamma(a,b), where a = 2 and 3 is an unknown parameter. 2 (a) Find the method of moments (MOM) estimator of B. (b) Find the maximum likelihood estimator (MLE) of B. (€) Are the estimators in parts (a) and (b) MVUEs for B? Justify your answer.
Problem 2. (10 points) Consider Yi .....Y a random sample of observations from a poisson distribution with un- known parameter . Find the MLE for ..