Homework Answers
Add Answer to:
You go out and collect the following data X = {21.12,..., 2n). Based on a review...
Please give detailed steps. Thank you. 5. Let {X, : i-1..n^ denote a random sample of...
Please give detailed steps. Thank you.
5. Let {X, : i-1..n^ denote a random sample of size n from a population described by a random varaible X following a Poisson(θ) distribution with PDF given by θ and var(X) θ (i.e. you do not You may take it as given that E(X) need to show these) a. Recall that an estimator is efficient, if it satisfies 2 conditions: 2) it achieves the Cramer-Rao Lower Bound (CLRB) for unbiased estimators: Show that...
Exercise: Let Yİ,Y2, ,, be a random sample from a Gamma distribution with parameters and β. Assum...
Exercise: Let Yİ,Y2, ,, be a random sample from a Gamma distribution with parameters and β. Assume α > 0 is known. a. Find the Maximum Likelihood Estimator for β. b. Show that the MLE is consistent for β. c. Find a sufficient statistic for β. d. Find a minimum variance unbiased estimator of β. e. Find a uniformly most powerful test for HO : β-2 vs. HA : β > 2. (Assume P(Type!Error)- 0.05, n 10 and a -...
2. (Discrete uniform). Consider the PMF P(X x)= for x 1,2,...0 _ You have a random...
2. (Discrete uniform). Consider the PMF P(X x)= for x 1,2,...0 _ You have a random sample of size three from this distribution: {2,3,10}. a. Find the method of moments estimate for 0 HINT: a very useful fact is that k1 n(n+1) 2 b. Find the MLE for 0 c. Which estimator is unbiased? d. Which estimator is preferred?
2. (Discrete uniform). Consider the PMF P(X x)= for x 1,2,...0 _ You have a random sample of size three from...
7. Let X1,....Xn random sample from a Bernoulli distribution with parameter p. A random variable X...
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...
(9) 112 pts] An exponentially distributed random variable, call it X, has the following probability density...
(9) 112 pts] An exponentially distributed random variable, call it X, has the following probability density function: f(x)-Be-ex , x > 0, θ > 0. Note that E(X) and VX-สั่ For the rest of this question, assume that you have a data set xn1 consisting of a random sample of N observations of X (a) Derive two different Method of Moments estimators for θ. HINT: remember that the MOM is based on the analogy principle, or the idea that sample...
(9) [12 pts] An exponentially distributed random variable, call it X, has the following probability density...
(9) [12 pts] An exponentially distributed random variable, call it X, has the following probability density functior f(x)-oe ex , x > 0, θ > 0 Note that ElX] and VX]ー1 For the rest of this question, assume that you have a data set (xn1 consisting of a random sample of N observations of X. (a) Derive two different Method of Moments estimators for θ. HINT: remember that the MOM is based on the analogy principle, or the idea that...
(9) 112 pts] An exponentially distributed random variable, call it X, has the following probability density...
(9) 112 pts] An exponentially distributed random variable, call it X, has the following probability density function: f(x)-Be-ex , x > 0, θ > 0. Note that E(X) and VX-สั่ For the rest of this question, assume that you have a data set xn1 consisting of a random sample of N observations of X (a) Derive two different Method of Moments estimators for θ. HINT: remember that the MOM is based on the analogy principle, or the idea that sample...
1. The size of claims made on an insurance policy are modelled through the following distribu- ti...
ANSWER QUESTION 2
1. The size of claims made on an insurance policy are modelled through the following distribu- tion: λ+1 You are interested in estimating the parameter λ > 0, using the following observations 120, 20, 60, 70, 110, 150, 220, 160, 100, 100 (a) Verify that f is a density (b) Find the expectation of the generic random variable X, as a function of when > 1 (c) Prove that the method of moments estimator of λ is...
For each of the following simulation studies, please try two different sample sizes (n = 30 and n...
For each of the following simulation studies, please try two different sample sizes (n = 30 and n = 300). When comparing the estimators, you need to consider both of the bias and variance of the estimates across 100 simulated samples with the same sizes. Please choose your own parameter(s) for the distributions. 1. Conduct a simulation study to compare the method of moment estimator and MLE for the parameters of a Beta distribution or Gamma distribution. (You only need...
For each of the following simulation studies, please try two different sample sizes (n = 30 and n...
For each of the following simulation studies, please try two different sample sizes (n = 30 and n = 300). When comparing the estimators, you need to consider both of the bias and variance of the estimates across 100 simulated samples with the same sizes. Please choose your own parameter(s) for the distributions. 1. Conduct a simulation study to compare the method of moment estimator and MLE for the parameters of a Beta distribution or Gamma distribution. (You only need...
Please give detailed steps. Thank you.
5. Let {X, : i-1..n^ denote a random sample of size n from a population described by a random varaible X following a Poisson(θ) distribution with PDF given by θ and var(X) θ (i.e. you do not You may take it as given that E(X) need to show these) a. Recall that an estimator is efficient, if it satisfies 2 conditions: 2) it achieves the Cramer-Rao Lower Bound (CLRB) for unbiased estimators: Show that...
Exercise: Let Yİ,Y2, ,, be a random sample from a Gamma distribution with parameters and β. Assume α > 0 is known. a. Find the Maximum Likelihood Estimator for β. b. Show that the MLE is consistent for β. c. Find a sufficient statistic for β. d. Find a minimum variance unbiased estimator of β. e. Find a uniformly most powerful test for HO : β-2 vs. HA : β > 2. (Assume P(Type!Error)- 0.05, n 10 and a -...
2. (Discrete uniform). Consider the PMF P(X x)= for x 1,2,...0 _ You have a random sample of size three from this distribution: {2,3,10}. a. Find the method of moments estimate for 0 HINT: a very useful fact is that k1 n(n+1) 2 b. Find the MLE for 0 c. Which estimator is unbiased? d. Which estimator is preferred?
2. (Discrete uniform). Consider the PMF P(X x)= for x 1,2,...0 _ You have a random sample of size three from...
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...
(9) 112 pts] An exponentially distributed random variable, call it X, has the following probability density function: f(x)-Be-ex , x > 0, θ > 0. Note that E(X) and VX-สั่ For the rest of this question, assume that you have a data set xn1 consisting of a random sample of N observations of X (a) Derive two different Method of Moments estimators for θ. HINT: remember that the MOM is based on the analogy principle, or the idea that sample...
(9) [12 pts] An exponentially distributed random variable, call it X, has the following probability density functior f(x)-oe ex , x > 0, θ > 0 Note that ElX] and VX]ー1 For the rest of this question, assume that you have a data set (xn1 consisting of a random sample of N observations of X. (a) Derive two different Method of Moments estimators for θ. HINT: remember that the MOM is based on the analogy principle, or the idea that...
(9) 112 pts] An exponentially distributed random variable, call it X, has the following probability density function: f(x)-Be-ex , x > 0, θ > 0. Note that E(X) and VX-สั่ For the rest of this question, assume that you have a data set xn1 consisting of a random sample of N observations of X (a) Derive two different Method of Moments estimators for θ. HINT: remember that the MOM is based on the analogy principle, or the idea that sample...
ANSWER QUESTION 2
1. The size of claims made on an insurance policy are modelled through the following distribu- tion: λ+1 You are interested in estimating the parameter λ > 0, using the following observations 120, 20, 60, 70, 110, 150, 220, 160, 100, 100 (a) Verify that f is a density (b) Find the expectation of the generic random variable X, as a function of when > 1 (c) Prove that the method of moments estimator of λ is...
For each of the following simulation studies, please try two different sample sizes (n = 30 and n = 300). When comparing the estimators, you need to consider both of the bias and variance of the estimates across 100 simulated samples with the same sizes. Please choose your own parameter(s) for the distributions. 1. Conduct a simulation study to compare the method of moment estimator and MLE for the parameters of a Beta distribution or Gamma distribution. (You only need...
For each of the following simulation studies, please try two different sample sizes (n = 30 and n = 300). When comparing the estimators, you need to consider both of the bias and variance of the estimates across 100 simulated samples with the same sizes. Please choose your own parameter(s) for the distributions. 1. Conduct a simulation study to compare the method of moment estimator and MLE for the parameters of a Beta distribution or Gamma distribution. (You only need...
Most questions answered within 3 hours.
-
1- What are 5 general characteristics of Botticelli’s
paintings?
2- Describe 5 important traits of Flemish...
asked 12 minutes ago -
A golfer claims that his average golf score at the course he
plays regularly is less...
asked 26 minutes ago -
On May 1, First Bank perfected a security interest in Debtor’s
inventory. On June 1, Bob...
asked 1 hour ago -
A new kind of typhoid shot is being developed by a medical
research team. The old...
asked 2 hours ago -
Write a chemical equation for these reactions. (Use
the lowest possible whole number coefficients.) Include
states-of-matter...
asked 4 hours ago -
For each of the Z-scores below, determine two probabilities
(show four three decimal places): (1) the...
asked 5 hours ago -
Oxidative phosphorylation is achieved through chemiosmotic
coupling, which turns chemical energy into osmotic potential energy
that...
asked 7 hours ago -
Hollywood Shoes would like to maintain their cash account at a
minimum level of $64,000, but...
asked 7 hours ago -
Proteins CtrA-P, DnaA, and GcrA behave similarly to what
molecule in the Eukaryotic Cell Cycle?
asked 7 hours ago -
TRUE OR FALSE
In case of a competitive tender procedure, in the request for
quotation, the...
asked 8 hours ago -
I am a little behind please provide some explanation, will
provide thumbs up.
This question considers...
asked 8 hours ago -
Let say the utility function as U(X,Y) = lnX + Y. Show that the
marginal rate...
asked 8 hours ago