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Let X denote the proportion of allotted time that a randomly selected student spends working on a certain aptitude test. Suppose the pdf of X is S(0 + f(x; 0) = 0 sx < 1 otherwise where -1 < 0. A random sample of ten students yields data x, = 0.73, x2 0.86, x3 = 0.94, x4 = 0.65, xs = 0.90, x6 = 0.49, x, = 0.99, xg = 0.92, x, = 0.79, x10 = 0.79 (a) Use the method of moments to obtain an estimator of 0 1 - 1 + X - 1 -1) 1 1 + X 1 - 2 - 1 1 - 2 1- Compute the estimate for this data. (Round your answer to two decimal places.) (b) Obtain the maximum likelihood estimator of 0. -n 1 Eln(X) Eln(X;) in Eln(X) Eln(X) -n Eln(X) 1 in Compute the estimate for the given data. (Round your answer to two decimal places.)

Let X denote the proportion of allotted time that a randomly selected student spends working on a certain aptitude test. Suppose the pdf of X is S(0 + f(x; 0) = 0 sx < 1 otherwise where -1 < 0. A random sample of ten students yields data x, = 0.73, x2 0.86, x3 = 0.94, x4 = 0.65, xs = 0.90, x6 = 0.49, x, = 0.99, xg = 0.92, x, = 0.79, x10 = 0.79 (a) Use the method of moments to obtain an estimator of 0 1 - 1 + X - 1 -1) 1 1 + X 1 - 2 - 1 1 - 2 1- Compute the estimate for this data. (Round your answer to two decimal places.) (b) Obtain the maximum likelihood estimator of 0. -n 1 Eln(X) Eln(X;) in Eln(X) Eln(X) -n Eln(X) 1 in Compute the estimate for the given data. (Round your answer to two decimal places.)

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Let X denote the proportion of allotted time that a randomly selected student spends working on a certain aptitude test. Suppose the pdf of X is S(0+ 1)xº 0 < x < 1 f(x; 0) otherwise where -1 < 0. A random sample of ten students yields data x, = 0.73, X2 = 0.86, x3 = 0.94, x4 = 0.65, x5 = 0.90, x6 = 0.49, x, = 0.99, xg = 0.92, x9 = 0.79, X10 = 0.79 (a) Use the method of moments to obtain an estimator of 0 1 - 1 1 + X 1 - 1 X - 1) 1 1 + - 2 X - 1 1 1 - X Compute the estimate for this data. (Round your answer to two decimal places.) (b) Obtain the maximum likelihood estimator of 0. -n - 1 Σn (X) Eln(X;) n Eln(X;) Eln(X;) -n ΣIn(X) - 1 n Compute the estimate for the given data. (Round your answer to two decimal places.)
Transcribed Image Text:Let X denote the proportion of allotted time that a randomly selected student spends working on a certain aptitude test. Suppose the pdf of X is S(0+ 1)xº 0 < x < 1 f(x; 0) otherwise where -1 < 0. A random sample of ten students yields data x, = 0.73, X2 = 0.86, x3 = 0.94, x4 = 0.65, x5 = 0.90, x6 = 0.49, x, = 0.99, xg = 0.92, x9 = 0.79, X10 = 0.79 (a) Use the method of moments to obtain an estimator of 0 1 - 1 1 + X 1 - 1 X - 1) 1 1 + - 2 X - 1 1 1 - X Compute the estimate for this data. (Round your answer to two decimal places.) (b) Obtain the maximum likelihood estimator of 0. -n - 1 Σn (X) Eln(X;) n Eln(X;) Eln(X;) -n ΣIn(X) - 1 n Compute the estimate for the given data. (Round your answer to two decimal places.)
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