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.)
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
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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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