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  3. 1 suppose that xi xn are a random sample having...

Question: 1 suppose that xi xn are a random sample having...

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1. Suppose that xi, ,xn are a random sample having probability density function Here the parameter θ > 0. (a) Determine the log likelibood, 10), and a 1- dimensional (a) Determine the log-likelihood, l(0), and a 1-dimensional sufficient statistic. (b) Show that P(XiS b;0) = +1 for f(x:0) given in (1). (c) Suppose now that because of a recurring computer glitch in storing the observations, only a random subset of the r, are observed. For the rest of the observations, it is only known that xi-1/2. Let δί-1 or 0 according to whether 2i is observed or not and let d Σίδί denote the number of x observed; thus n - d of the a are only known to satisfy i K 1/2. Determine the likelihood, L(0), and a 2-dimensional sufficient statistic. Note that d is a random quantity dependent on the data. You can use the result of (b) even if you were unable to show it.

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