27. 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 f(x; 0) = (0+1)xº 0≤x≤1 for some > -1. A random sample of ten students yields data x₁ = .92, x₂ = .79, X3 = .90, X4 = .65, x5 = .86, x6 = .47, X7 = .73, x8 = .97, x9 = .94, X10 = .77. a. Use the method of moments to obtain an estimator of 0, and then compute the estimate for this data. b. Obtain the maximum likelihood esti- mator of 0, and then compute the esti- mate for the given data.
27. 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 f(x; 0) = (0+1)xº 0≤x≤1 for some > -1. A random sample of ten students yields data x₁ = .92, x₂ = .79, X3 = .90, X4 = .65, x5 = .86, x6 = .47, X7 = .73, x8 = .97, x9 = .94, X10 = .77. a. Use the method of moments to obtain an estimator of 0, and then compute the estimate for this data. b. Obtain the maximum likelihood esti- mator of 0, and then compute the esti- mate for the given data.
Calculus For The Life Sciences
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Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
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Chapter2: Exponential, Logarithmic, And Trigonometric Functions
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Transcribed Image Text:27. 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
f(x; 0) = (0+1)xº 0≤x≤1
for some > -1. A random sample of ten
students yields data x₁ = .92, x₂ = .79,
X3 = .90, X4 = .65, x5 = .86, x6 = .47,
X7 = .73, x8 = .97, x9 = .94, X10 = .77.
a. Use the method of moments to obtain an
estimator of 0, and then compute the
estimate for this data.
b. Obtain the maximum likelihood esti-
mator of 0, and then compute the esti-
mate for the given data.
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