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4. Suppose that a population U is divided into 2 subgroups (PSUs), each of which contains...
CLUSTER SAMPLING WITH ESTIMATION Suppose a population of size N is divided into K- N/M groups of size M. We select a sample of size n -km the following way: » First we select k groups out of K groups...
CLUSTER SAMPLING WITH ESTIMATION Suppose a population of size N is divided into K- N/M groups of size M. We select a sample of size n -km the following way: » First we select k groups out of K groups by simple random sampling . We then select m units in each group selected on the first step by simple random sampling . The estimate of the population mean is the average Y of the sample. Let μί be the...
Please give detailed steps. Thank you. 5. Let {X1, X2,..., Xn) denote a random sample of...
Please give detailed steps. Thank you.
5. Let {X1, X2,..., Xn) denote a random sample of size N from a population d escribed by a random variable X. Let's denote the population mean of X by E(X) - u and its variance by Consider the following four estimators of the population mean μ : 3 (this is an example of an average using only part of the sample the last 3 observations) (this is an example of a weighted average)...
Find a consistent estimator of µ 2 , where E(Y ) = µ is the population mean and Y¯ n is the sample mean. 2 If E(Y 2 ) =...
Find a consistent estimator of µ 2 , where E(Y ) = µ is the
population mean and Y¯ n is the sample mean. 2 If E(Y 2 ) = µ 0 2
then prove that 1 n Pn i=1 Y 2 i is an consistent estimator of µ 0
2 3 We define σ 2 = µ 0 2 − µ 2 . Show that S 2 n = 1 n Pn i=1 Y 2
i − Y¯ 2...
Problem 2. Suppose the population has six units: U={1,2,3,4,5,6} and samples of size 3 could be...
Problem 2. Suppose the population has six units: U={1,2,3,4,5,6} and samples of size 3 could be chosen from this population. For purposes of studying sampling distribution, assume that all population values are known y1 92 , y2 = 108, y3 = 154, y4 = 133, y5 = 190, y6 = 175 We are interested in yu, the population mean. One sampling plan is proposed. Sample, S (1,3,5 {1,4,6 {2,3,6 (2,4,5 P(S) Sample Number 1 0.25 2 0.2 3 0.2 0.35...
3. (5 marks) Let U be a random variable which has the continuous uniform distribution on the inte...
3. (5 marks) Let U be a random variable which has the continuous uniform distribution on the interval I-1, 1]. Recall that this means the density function fu satisfies for(z-a: a.crwise. 1 u(z), -1ss1, a) Find thc cxpccted valuc and the variancc of U. We now consider estimators for the expected value of U which use a sample of size 2 Let Xi and X2 be independent random variables with the same distribution as U. Let X = (X1 +...
5. Horvitz-Thompson (HT) estimator (a) (2 marks) Show that the HT estimator es tu/su is unbiased...
5. Horvitz-Thompson (HT) estimator (a) (2 marks) Show that the HT estimator es tu/su is unbiased for the population total. Clearly define any notation used. (b) (1 mark) The variance of the HT estimator is Var(ār(s)) = () Give the HT estimate of the variance based on the sample, S. (c) (1 mark) Suppose we sample with replacement where probability of selecting unit u is pu. Derive the inclusion probability for unit. (d) A sample (n = 6) was randomly...
I REALLY need numbers 2 and 3 and 5 by like tomorrow morning. I have no...
I REALLY need numbers 2 and 3 and 5 by like tomorrow morning.
I have no clue how to do these. I know the image quality is iffy
but please help as best you can
Homework1 STA4322 Homework 1, Spring 2019 Please turn in your own work, though you may discuss the problems with classmates, the TA, the Professor, the internet, etc. The most important thing is that you understand the problems and how they are solved as they will...
I figured out 1,2 and 3 but I’m stuck on 4 and 5. Please help me...
I
figured out 1,2 and 3 but I’m stuck on 4 and 5. Please help me out
if you can!! I know the quality isn’t the greatest, I’m sorry!!
Homework1 STA4322 Homework 1, Spring 2019 Please turn in your own work, though you may discuss the problems with classmates, the TA, the Professor, the internet, etc. The most important thing is that you understand the problems and how they are solved as they will prepare you for the exam. Please...
1. In the simple regression model y = + β1x + u, suppose that E (u)...
1. In the simple regression model y = + β1x + u, suppose that E (u) 0. Letting oo-E(u), show that the model can always be rewrit ten with the same slope, but a new intercept and error, where the new error has a zero expected value 2. The data set BWGHT contains data on births to women in the United States. Two variables of interest are the dependent variable, nfan birth weight in ounces (bught), and an explanatory variable,...
Problem 2. Consider the following joint probabilities for the two variables X and Y. 1 2...
Problem 2. Consider the following joint probabilities for the two variables X and Y. 1 2 3 .14 .25 .01 2 33 .10 .07 3 .03 .05 .02 Find the marginal probability distribution of Y and graph it. Show your calculations. b. Find the conditional probability distribution of Y (given that X = 2) and graph it. Show your calculations. c. Do your results in (a) and (b) satisfy the probability distribution requirements? Explain clearly. d. Find the correlation coefficient...
CLUSTER SAMPLING WITH ESTIMATION Suppose a population of size N is divided into K- N/M groups of size M. We select a sample of size n -km the following way: » First we select k groups out of K groups by simple random sampling . We then select m units in each group selected on the first step by simple random sampling . The estimate of the population mean is the average Y of the sample. Let μί be the...
Please give detailed steps. Thank you.
5. Let {X1, X2,..., Xn) denote a random sample of size N from a population d escribed by a random variable X. Let's denote the population mean of X by E(X) - u and its variance by Consider the following four estimators of the population mean μ : 3 (this is an example of an average using only part of the sample the last 3 observations) (this is an example of a weighted average)...
Find a consistent estimator of µ 2 , where E(Y ) = µ is the
population mean and Y¯ n is the sample mean. 2 If E(Y 2 ) = µ 0 2
then prove that 1 n Pn i=1 Y 2 i is an consistent estimator of µ 0
2 3 We define σ 2 = µ 0 2 − µ 2 . Show that S 2 n = 1 n Pn i=1 Y 2
i − Y¯ 2...
Problem 2. Suppose the population has six units: U={1,2,3,4,5,6} and samples of size 3 could be chosen from this population. For purposes of studying sampling distribution, assume that all population values are known y1 92 , y2 = 108, y3 = 154, y4 = 133, y5 = 190, y6 = 175 We are interested in yu, the population mean. One sampling plan is proposed. Sample, S (1,3,5 {1,4,6 {2,3,6 (2,4,5 P(S) Sample Number 1 0.25 2 0.2 3 0.2 0.35...
3. (5 marks) Let U be a random variable which has the continuous uniform distribution on the interval I-1, 1]. Recall that this means the density function fu satisfies for(z-a: a.crwise. 1 u(z), -1ss1, a) Find thc cxpccted valuc and the variancc of U. We now consider estimators for the expected value of U which use a sample of size 2 Let Xi and X2 be independent random variables with the same distribution as U. Let X = (X1 +...
5. Horvitz-Thompson (HT) estimator (a) (2 marks) Show that the HT estimator es tu/su is unbiased for the population total. Clearly define any notation used. (b) (1 mark) The variance of the HT estimator is Var(ār(s)) = () Give the HT estimate of the variance based on the sample, S. (c) (1 mark) Suppose we sample with replacement where probability of selecting unit u is pu. Derive the inclusion probability for unit. (d) A sample (n = 6) was randomly...
I REALLY need numbers 2 and 3 and 5 by like tomorrow morning.
I have no clue how to do these. I know the image quality is iffy
but please help as best you can
Homework1 STA4322 Homework 1, Spring 2019 Please turn in your own work, though you may discuss the problems with classmates, the TA, the Professor, the internet, etc. The most important thing is that you understand the problems and how they are solved as they will...
I
figured out 1,2 and 3 but I’m stuck on 4 and 5. Please help me out
if you can!! I know the quality isn’t the greatest, I’m sorry!!
Homework1 STA4322 Homework 1, Spring 2019 Please turn in your own work, though you may discuss the problems with classmates, the TA, the Professor, the internet, etc. The most important thing is that you understand the problems and how they are solved as they will prepare you for the exam. Please...
1. In the simple regression model y = + β1x + u, suppose that E (u) 0. Letting oo-E(u), show that the model can always be rewrit ten with the same slope, but a new intercept and error, where the new error has a zero expected value 2. The data set BWGHT contains data on births to women in the United States. Two variables of interest are the dependent variable, nfan birth weight in ounces (bught), and an explanatory variable,...
Problem 2. Consider the following joint probabilities for the two variables X and Y. 1 2 3 .14 .25 .01 2 33 .10 .07 3 .03 .05 .02 Find the marginal probability distribution of Y and graph it. Show your calculations. b. Find the conditional probability distribution of Y (given that X = 2) and graph it. Show your calculations. c. Do your results in (a) and (b) satisfy the probability distribution requirements? Explain clearly. d. Find the correlation coefficient...
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