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4. Let X denote the proportion of allotted time that a randomly selected student spends working on a class test. Suppose
Posted: Thu May 05, 2022 8:08 pm
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4. Let X denote the proportion of allotted time that a randomly selected student spends working on a class test. Suppose the probability density function of X is f(x; λ) = (2+1)x¹; 0≤x≤1 where the parameter > > -1. A random sample of students yields the data: x₁ = .82; X₂=.79: x3 = .90; X4 = .65; XS = .76; x6 = 47; X7=.73: X = .87; X = .74; X10 = .77. (a) Use the method of moments to find an estimator for A and then use this and the data above to calculate an estimate. [5 Marks] (b) Find the maximum likelihood estimator for A and then use the data to calculate an estimate using this estimator. [6 Marks]