You are interested in the average amount of money Queen's students made during the summer. Assume...
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You are interested in the average amount of money Queen's students made during the summer. Assume the population mean is μ and variance ². You don't want to ask everyone in the population (all Queen's students), so you decide to randomly ask 5 people. Denote their summer income as Y₁, Y₂, Y3, Y₁, and Y5. Consider an estimator W₁ which is equal to the sample average income, (Y₁ + Y₂ + Y3 + Y4 + Y5). What are the expected value and variance of W₁ in terms of u and 2? Is the estimator unbiased estimator of the population mean? + Drag and drop an image or PDF file or click to browse... Q1 b (5 points) Consider another estimator, W₂ which is just simply equal to the first student you asked (Y₁). What are the expected value and variance of W₂ in terms of u and o2? Is this estimator of the population mean unbiased? Q1 c (5 points) Now consider a different estimator, call it W3, which is equal to a weighted average of each of the students you asked. W₂ = ₁ + ² Y₂ + Y3 + 1 Y ₁ + Y Is W3 an unbiased estimator of the population mean? Q1 d (5 points) + Drag and drop an image or PDF file or click to browse... Which of these three estimators do you think is the best estimator of the population mean You are interested in the average amount of money Queen's students made during the summer. Assume the population mean is μ and variance ². You don't want to ask everyone in the population (all Queen's students), so you decide to randomly ask 5 people. Denote their summer income as Y₁, Y₂, Y3, Y₁, and Y5. Consider an estimator W₁ which is equal to the sample average income, (Y₁ + Y₂ + Y3 + Y4 + Y5). What are the expected value and variance of W₁ in terms of u and 2? Is the estimator unbiased estimator of the population mean? + Drag and drop an image or PDF file or click to browse... Q1 b (5 points) Consider another estimator, W₂ which is just simply equal to the first student you asked (Y₁). What are the expected value and variance of W₂ in terms of u and o2? Is this estimator of the population mean unbiased? Q1 c (5 points) Now consider a different estimator, call it W3, which is equal to a weighted average of each of the students you asked. W₂ = ₁ + ² Y₂ + Y3 + 1 Y ₁ + Y Is W3 an unbiased estimator of the population mean? Q1 d (5 points) + Drag and drop an image or PDF file or click to browse... Which of these three estimators do you think is the best estimator of the population mean
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To find the expected value and variance of the estimator W which is the sample average income we can ... View the full answer
Related Book For
Statistics For Business And Economics
ISBN: 9780132745659
8th Edition
Authors: Paul Newbold, William Carlson, Betty Thorne
Posted Date:
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