Let X be a discrete random variable with the pmf as given below, for 0 <0<1. 3 4 0 1-0 30 3(1– 0) P(X = x) Six independent observations were taken from this distribution, as follows: 2, 3, 1, 1, 4, 2. (a) Obtain the likelihood function, L(0). (b) Show that the log-likelihood ((0) is e(0) = C +3 log 0 + 3 log(1 – 0), where C is a constant not involving 0. Hence give the value of C. (c) Find (@) and hence the candidate MLE, 6, of 0. (d) Confirm that the candidate MLE, 6, that you found in part (c), is indeed the MILE of 0.
Let X be a discrete random variable with the pmf as given below, for 0 <0<1. 3 4 0 1-0 30 3(1– 0) P(X = x) Six independent observations were taken from this distribution, as follows: 2, 3, 1, 1, 4, 2. (a) Obtain the likelihood function, L(0). (b) Show that the log-likelihood ((0) is e(0) = C +3 log 0 + 3 log(1 – 0), where C is a constant not involving 0. Hence give the value of C. (c) Find (@) and hence the candidate MLE, 6, of 0. (d) Confirm that the candidate MLE, 6, that you found in part (c), is indeed the MILE of 0.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text:Let X be a discrete random variable with the pmf as given below,
for 0 <0 <1.
1
O 1-0 30 3(1 – 6)
2
3
4
P(X = x)
Six independent observations were taken from this distribution, as follows:
2, 3, 1, 1, 4, 2.
(a) Obtain the likelihood function, L(0).
(b) Show that the log-likelihood €(0) is
e(0) = C + 3 log 0 + 3 log(1 – 6),
where C is a constant not involving 0. Hence give the value of C.
(e) Find l (0) and hence the candidate MLE, ô, of 0.
(d) Confirm that the candidate MLE, ô0, that you found in part (c), is
indeed the MLE of 0.
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