Problem #3: 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 Problem #3(a): Problem #3(b): f(x; 0) = (0+1)x 0 0≤x≤1 otherwise where > -1. A random sample of ten students yields the data 0.42, 0.60, 0.57, 0.67, 0.80, 0.59, 0.70, 0.53, 0.96, 0.51 (a) Use the method of moments to obtain an estimator for 8, and then use it to compute an estimate from the data. (b) Find the maximum likelihood estimator for 8, and then use it to compute an estimate for from the data. answer correct to 2 decimals

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Problem #3: 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
Problem #3(a):
Problem #3(b):
f(x; 0) =
(0+1)x
0
0 ≤ x ≤ 1
otherwise
where > -1. A random sample of ten students yields the data
0.42, 0.60, 0.57, 0.67, 0.80, 0.59, 0.70, 0.53, 0.96, 0.51
(a) Use the method of moments to obtain an estimator for 0, and then use it to compute an estimate from the data.
(b) Find the maximum likelihood estimator for 0, and then use it to compute an estimate for from the data.
answer correct to 2 decimals
answer correct to 2 decimals
Transcribed Image Text:Problem #3: 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 Problem #3(a): Problem #3(b): f(x; 0) = (0+1)x 0 0 ≤ x ≤ 1 otherwise where > -1. A random sample of ten students yields the data 0.42, 0.60, 0.57, 0.67, 0.80, 0.59, 0.70, 0.53, 0.96, 0.51 (a) Use the method of moments to obtain an estimator for 0, and then use it to compute an estimate from the data. (b) Find the maximum likelihood estimator for 0, and then use it to compute an estimate for from the data. answer correct to 2 decimals answer correct to 2 decimals
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