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.
Homework Answers
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previously, the problem b1(a) is Suppose that we know Y has a
Geometric distribution with parameter...
question： B1. A random sample of n observations, Yi, ..., Yn, is selected from a pop-...
question：
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. C3. Continue with Problem B1 (a), Homework 2. Find the MLE of p.
B1. A random sample of n observations, Yi, ., Yn, is selected from a pop- ulation...
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...
Al. A random sample of n observations, Yi, ..., Yn, is selected from a pop- ulation...
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...
QUESTION： Yi, Y2, Y, denote a random sample from the normal distribution with known mean μ...
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.
4. We have n independent observations from a geometric distribution with unknown parameter θ. PoX, k...
4. We have n independent observations from a geometric distribution with unknown parameter θ. PoX, k 0(1- 0)1 or1,2,3,... We wish to test the null hypothesis θ-1/2 versus the alternative θ 1 /2. we can show that the MLE θ-1/2. Write out the appropriate LRT statistic as a function of the x, the mean of the observations
4. We have n independent observations from a geometric distribution with unknown parameter θ. PoX, k...
4. We have n independent observations from a geometric distribution with unknown parameter θ. PoX, k 0(1- 0)1 or1,2,3,... We wish to test the null hypothesis θ-1/2 versus the alternative θ 1 /2. we can show that the MLE θ-1/2. Write out the appropriate LRT statistic as a function of the x, the mean of the observations
4. We have n independent observations from a geometric distribution with unknown parameter Pe(X = k}...
4. We have n independent observations from a geometric distribution with unknown parameter Pe(X = k} = θ(1-0)k-1 for k = 1.2.3. We wish to test the null hypothesis θ-1/2 versus the alternative θ 1/2, we can show that the MLE θ = 1/z. write out the appropriate LRT, statistic as a function of the z, the mean of the observations.
I. Consider a variable y = θ + where θ is an unknown parameter and e is a random variable with me...
I. Consider a variable y = θ + where θ is an unknown parameter and e is a random variable with mean zero. (a) What is the expected value of y? (b) Suppose you draw a sample of yi yn. Derive the least squares estimator for θ. For full credit you must check the 2nd order condition c) Can this estimator (0) be described as a method of moments estimator? (d) Now suppose є is independent normally distributed with mean...
Problem 2. Rice, Problem 7, pg. 314 (Extended)] Suppose that X1,..., Xn iid Geometric(p). a) Find...
Problem 2. Rice, Problem 7, pg. 314 (Extended)] Suppose that X1,..., Xn iid Geometric(p). a) Find the method of moments estimator for p. (b) Find the maximum likelihood estimator for p. (c) Find the asymptotic variance of the MLE (d) Suppose that p has a uniform prior distribution on the interval [0, 1]. What is the posterior distribution of p? For part (e), assume that we obtained a random sample of size 4 with L^^^xi-.4 (e) What is the posterior...
4. (9 pts) Suppose the random variable Y has a geometric distribution with parameter p. Let...
4. (9 pts) Suppose the random variable Y has a geometric
distribution with parameter p. Let ?? = √?? 3 3 . Find the
probability distribution of V
3 4. (9 pts) Suppose the random variable Y has a geometric distribution with parameter p. Let V 3 Find the probability distribution of.
question：
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. C3. Continue with Problem B1 (a), Homework 2. Find the MLE of p.
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...
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...
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.
4. We have n independent observations from a geometric distribution with unknown parameter θ. PoX, k 0(1- 0)1 or1,2,3,... We wish to test the null hypothesis θ-1/2 versus the alternative θ 1 /2. we can show that the MLE θ-1/2. Write out the appropriate LRT statistic as a function of the x, the mean of the observations
4. We have n independent observations from a geometric distribution with unknown parameter θ. PoX, k 0(1- 0)1 or1,2,3,... We wish to test the null hypothesis θ-1/2 versus the alternative θ 1 /2. we can show that the MLE θ-1/2. Write out the appropriate LRT statistic as a function of the x, the mean of the observations
4. We have n independent observations from a geometric distribution with unknown parameter Pe(X = k} = θ(1-0)k-1 for k = 1.2.3. We wish to test the null hypothesis θ-1/2 versus the alternative θ 1/2, we can show that the MLE θ = 1/z. write out the appropriate LRT, statistic as a function of the z, the mean of the observations.
I. Consider a variable y = θ + where θ is an unknown parameter and e is a random variable with mean zero. (a) What is the expected value of y? (b) Suppose you draw a sample of yi yn. Derive the least squares estimator for θ. For full credit you must check the 2nd order condition c) Can this estimator (0) be described as a method of moments estimator? (d) Now suppose є is independent normally distributed with mean...
Problem 2. Rice, Problem 7, pg. 314 (Extended)] Suppose that X1,..., Xn iid Geometric(p). a) Find the method of moments estimator for p. (b) Find the maximum likelihood estimator for p. (c) Find the asymptotic variance of the MLE (d) Suppose that p has a uniform prior distribution on the interval [0, 1]. What is the posterior distribution of p? For part (e), assume that we obtained a random sample of size 4 with L^^^xi-.4 (e) What is the posterior...
4. (9 pts) Suppose the random variable Y has a geometric
distribution with parameter p. Let ?? = √?? 3 3 . Find the
probability distribution of V
3 4. (9 pts) Suppose the random variable Y has a geometric distribution with parameter p. Let V 3 Find the probability distribution of.
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