Q2. Suppose you have the same pdf given in Q1 with known B. The goal is to estimate the unknown 0. But suppose that, instead of observing X1,...,X, exactly, you only get to see whether or not each X; is less than 5. That is, you only observe Y1,..., Ym where 19• • (1, X, 5 5 Y, =. 0, X, > 5 ,i = 1,..., n. a) What is the distribution from which Y1,..., Y, is sampled? 19•••, n b) Using the corrupted data Y,...,Y, only, discuss how to find the numeric values of the MLE 0.

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Q1. Let X,..,X, are iid from a distribution with
pdf
F(xe) = 9B°
X2 β
where B and 0
are positive unknown
parameters.
Transcribed Image Text:Q1. Let X,..,X, are iid from a distribution with pdf F(xe) = 9B° X2 β where B and 0 are positive unknown parameters.
Q2. Suppose you have the same pdf given in Q1
with known ß. The goal is to estimate the
unknown 0. But suppose that, instead of observing
X1,...,X, exactly, you only get to see whether or
not each X; is less than 5. That is, you only observe
Y,..., Y, where
1, X; < 5
Y,
0, Х, > 5
i = 1,..., n.
a) What is the distribution from which
Y1,..., Y, is sampled?
• • •
b) Using the corrupted data Y1,...,Y, only,
discuss how to find the numeric values of the
MLE 0.
Transcribed Image Text:Q2. Suppose you have the same pdf given in Q1 with known ß. The goal is to estimate the unknown 0. But suppose that, instead of observing X1,...,X, exactly, you only get to see whether or not each X; is less than 5. That is, you only observe Y,..., Y, where 1, X; < 5 Y, 0, Х, > 5 i = 1,..., n. a) What is the distribution from which Y1,..., Y, is sampled? • • • b) Using the corrupted data Y1,...,Y, only, discuss how to find the numeric values of the MLE 0.
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