Let X₁,..., Xn be a random sample from a distribution with one of two pdfs. If 0 = 1, then f(x;0=1) = 1 (0 < x < 1). If 0 = 2, then f(x;0= 2) = 2x1 (0 < x < 1). (a) Give a general form of the MLE of 0. (b) You are given a sample data of 3 values: 0.4, 0.5, 0.8. Find the MLE estimate of 0 based on the data.

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Let X₁,..., Xn be a random sample from a distribution with one of two pdfs. If 0 = 1, then
f(x;0=1) = 1 (0 < x < 1). If 0 = 2, then f(x;0= 2) = 2x1 (0 < x < 1).
(a) Give a general form of the MLE of 0.
(b) You are given a sample data of 3 values: 0.4, 0.5, 0.8. Find the MLE estimate of 0 based
on the data.
Transcribed Image Text:Let X₁,..., Xn be a random sample from a distribution with one of two pdfs. If 0 = 1, then f(x;0=1) = 1 (0 < x < 1). If 0 = 2, then f(x;0= 2) = 2x1 (0 < x < 1). (a) Give a general form of the MLE of 0. (b) You are given a sample data of 3 values: 0.4, 0.5, 0.8. Find the MLE estimate of 0 based on the data.
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