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Consider the random variable X with density given by f(x) = θ 2xe−θx x > 0,...

Consider the random variable X with density given by f(x) = θ 2xe−θx x > 0, θ > 0 a) Derive the expression for E(X). b) Find the method of moment estimator for θ. c) Find the maximum likelihood estimator for θ based on a random sample of size n. Does this estimator differ from that found in part (b)? d) Estimate θ based on the following data: 0.1, 0.3, 0.5, 0.2, 0.3, 0.4, 0.4, 0.3, 0.3, 0.3

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