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Now suppose that the quantity you really want to estimate is the square of the population...
Estimator properties: 6 Estimators properties 6.1 Exercise 1 In order to estimate the average number of...
Estimator properties:
6 Estimators properties 6.1 Exercise 1 In order to estimate the average number of hours that children spend watching tv, a Bernoulli sample of size n = 5 children was selected from a primary school. Let X be the variable that represents the hours spent watching tv, let E(X)-μ the parameter to estimate and var(X-σ2 the variance. Compare the following two proposed estimators Τι 1. Compare the two estimators for u on the basis of their bias 2....
Let Y, Y2, ..., Yn be n i.i.d random variables drawn from the population distribution of...
Let Y, Y2, ..., Yn be n i.i.d random variables drawn from the population distribution of Y-(My, oy). Suppose we want to estimate My and we are asked to choose between two possible estimators of Wy: (1)Y, and (2) Y = (x + 3) (a) Show both estimators are unbiased (2 points) (b) Derive the variance of both estimators and discuss which estimator is more efficient (3 points)
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)...
1. Suppose a population of N individuals has true (unknown) numerical measurements yi, y2, …YN (repeats...
1. Suppose a population of N individuals has true (unknown) numerical measurements yi, y2, …YN (repeats allowed). The unknown population mean 1S yj One way to estimate the unknown population mean μ is to decide on a number nS N, then successively randomly select one individual at a time, observe and record the quantity of interest for that individual, put that individual back in, and repeat the process n times. Then form the mean of the recorded n observations. Prove...
|Suppose that you want to estimate the integral 1 1+]da I Unif (0,1) sample: (a) The...
|Suppose that you want to estimate the integral 1 1+]da I Unif (0,1) sample: (a) The following numbers are a 0.42 0.73 0.89 0.11 Use the Monte Carlo method from class to approximate the integral via the estimator I4 (b) Now make n really big and see if you can get me a really good answer.
|Suppose that you want to estimate the integral 1 1+]da I
Unif (0,1) sample: (a) The following numbers are a 0.42 0.73 0.89 0.11...
You observe sarriples X1....,x. Ber(@) where 0 € (0,1) is an unknown parameter. Suppose that is...
You observe sarriples X1....,x. Ber(@) where 0 € (0,1) is an unknown parameter. Suppose that is much larger than 1 so we have access to many samples from the specified distribution. Consider three candidate estimators for 0. . X.-1x . 0.5 In the next three questions, you will consider potential strengths and weaknesses of these estimators. In this particular section (just for now), the phrase "efficiently computable" refers to the existence of an explicit formula. More precisely, here we say...
Let Y, Y2, Yz and Y4 be independent, identically distributed random variables from a population with...
Let Y, Y2, Yz and Y4 be independent, identically distributed random variables from a population with mean u and variance o. Let Y = -(Y, + Y2 + Y3 +Y4) denote the average of these four random variables. i. What are the expected value and variance of 7 in terms of u and o? ii. Now consider a different estimator of u: W = y + y + y +Y4 This an example of weighted average of the Y. Show...
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...
1) You want to obtain a sample to estimate a population mean. Based on previous evidence,...
1) You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately σ=20.5σ=20.5. You would like to be 90% confident that your esimate is within 10 of the true population mean. How large of a sample size is required? n = Use a critical value accurate to three decimal places, and do not round mid-calculation — this is important for the system to be able to give hints...
18) Suppose you want to estimate the proportion of a population who had engaged in a...
18) Suppose you want to estimate the proportion of a population who had engaged in a sensitive or embarrassing activity. You randomly select n 120 subjects. They roll a die: Rolls of 1 or 2 require them to answer "Yes." Rolls of 3 or 4 require a "No" answer. And on rolls of 5 or 6 they are instructed to tell the truth. Here are the results: 68 YES; 52 NO. What estimated sample proportion of Yes's does this imply?...
Estimator properties:
6 Estimators properties 6.1 Exercise 1 In order to estimate the average number of hours that children spend watching tv, a Bernoulli sample of size n = 5 children was selected from a primary school. Let X be the variable that represents the hours spent watching tv, let E(X)-μ the parameter to estimate and var(X-σ2 the variance. Compare the following two proposed estimators Τι 1. Compare the two estimators for u on the basis of their bias 2....
Let Y, Y2, ..., Yn be n i.i.d random variables drawn from the population distribution of Y-(My, oy). Suppose we want to estimate My and we are asked to choose between two possible estimators of Wy: (1)Y, and (2) Y = (x + 3) (a) Show both estimators are unbiased (2 points) (b) Derive the variance of both estimators and discuss which estimator is more efficient (3 points)
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)...
1. Suppose a population of N individuals has true (unknown) numerical measurements yi, y2, …YN (repeats allowed). The unknown population mean 1S yj One way to estimate the unknown population mean μ is to decide on a number nS N, then successively randomly select one individual at a time, observe and record the quantity of interest for that individual, put that individual back in, and repeat the process n times. Then form the mean of the recorded n observations. Prove...
|Suppose that you want to estimate the integral 1 1+]da I Unif (0,1) sample: (a) The following numbers are a 0.42 0.73 0.89 0.11 Use the Monte Carlo method from class to approximate the integral via the estimator I4 (b) Now make n really big and see if you can get me a really good answer.
|Suppose that you want to estimate the integral 1 1+]da I
Unif (0,1) sample: (a) The following numbers are a 0.42 0.73 0.89 0.11...
You observe sarriples X1....,x. Ber(@) where 0 € (0,1) is an unknown parameter. Suppose that is much larger than 1 so we have access to many samples from the specified distribution. Consider three candidate estimators for 0. . X.-1x . 0.5 In the next three questions, you will consider potential strengths and weaknesses of these estimators. In this particular section (just for now), the phrase "efficiently computable" refers to the existence of an explicit formula. More precisely, here we say...
Let Y, Y2, Yz and Y4 be independent, identically distributed random variables from a population with mean u and variance o. Let Y = -(Y, + Y2 + Y3 +Y4) denote the average of these four random variables. i. What are the expected value and variance of 7 in terms of u and o? ii. Now consider a different estimator of u: W = y + y + y +Y4 This an example of weighted average of the Y. Show...
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...
18) Suppose you want to estimate the proportion of a population who had engaged in a sensitive or embarrassing activity. You randomly select n 120 subjects. They roll a die: Rolls of 1 or 2 require them to answer "Yes." Rolls of 3 or 4 require a "No" answer. And on rolls of 5 or 6 they are instructed to tell the truth. Here are the results: 68 YES; 52 NO. What estimated sample proportion of Yes's does this imply?...
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