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Exercise 1 Suppose you have a random sample 1....Un of 100 observations from a normal distribution with unknown mean and unknown standard deviation o. You want to estimate these two parameters using both maximum likelihood estimation (MLE) and method of moments (MoM). 1. Write down the likelihood function for the sample. 2. Using MLE, find the estimates of u and o. 3. Using MoM, find the estimates of u and a. 4. Compare the estimates obtained using MLE and MoM. 5. Can you answer the same questions as above if we assume the random sample is generated from the following density function: f(a; a)= a(a + 1)2-1(1-x)

Exercise 1 Suppose you have a random sample 1....Un of 100 observations from a normal distribution with unknown mean and unknown standard deviation o. You want to estimate these two parameters using both maximum likelihood estimation (MLE) and method of moments (MoM). 1. Write down the likelihood function for the sample. 2. Using MLE, find the estimates of u and o. 3. Using MoM, find the estimates of u and a. 4. Compare the estimates obtained using MLE and MoM. 5. Can you answer the same questions as above if we assume the random sample is generated from the following density function: f(a; a)= a(a + 1)2-1(1-x)

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 22PFA
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Exercise 1 Suppose you have a random sample ₁₁ unknown mean maximum likelihood estimation (MLE) and method of moments (MoM). of 100 observations from a normal distribution with and unknown standard deviation o. You want to estimate these two parameters using both 1. Write down the likelihood function for the sample. 2. Using MLE, find the estimates of u and o. 3. Using MoM, find the estimates of u and o. 4. Compare the estimates obtained using MLE and MoM. 5. Can you answer the same questions as above if we assume the random sample is generated from the following density function: f(x; a)= a(a + 1)-¹(1-x) if a € (0, 1) and f(x: a) =) elsewhere and where a > 0 is the unknown parameter.
Transcribed Image Text:Exercise 1 Suppose you have a random sample ₁₁ unknown mean maximum likelihood estimation (MLE) and method of moments (MoM). of 100 observations from a normal distribution with and unknown standard deviation o. You want to estimate these two parameters using both 1. Write down the likelihood function for the sample. 2. Using MLE, find the estimates of u and o. 3. Using MoM, find the estimates of u and o. 4. Compare the estimates obtained using MLE and MoM. 5. Can you answer the same questions as above if we assume the random sample is generated from the following density function: f(x; a)= a(a + 1)-¹(1-x) if a € (0, 1) and f(x: a) =) elsewhere and where a > 0 is the unknown parameter.
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