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Suppose that X1, X2, . . . , Xm, representing yields per
Chapter 9, Problem 86E(choose chapter or problem)
Problem 86E
Suppose that X1, X2, . . . , Xm, representing yields per acre for corn variety A, constitute a random sample from a normal distribution with mean μ1 and variance σ 2. Also, Y1 Y2, . . . , Yn, representing yields for corn variety B, constitute a random sample from a normal distribution with mean μ2 and variance σ 2. If the X ’s and Y ’s are independent, find the MLE for the common variance σ 2. Assume that μ1 and μ2 are unknown.
Questions & Answers
QUESTION:
Problem 86E
Suppose that X1, X2, . . . , Xm, representing yields per acre for corn variety A, constitute a random sample from a normal distribution with mean μ1 and variance σ 2. Also, Y1 Y2, . . . , Yn, representing yields for corn variety B, constitute a random sample from a normal distribution with mean μ2 and variance σ 2. If the X ’s and Y ’s are independent, find the MLE for the common variance σ 2. Assume that μ1 and μ2 are unknown.
ANSWER:
Step 1 of 3
According to the concept,
We need to just multiply the two density function and get:
Now,