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Mathematics, 30.11.2019 05:40 palcochran1313

You go out and collect the following data x = {x1, x2, xn}. based on a review of existing literature, you decide that your data could follow a rayleigh distribution: f(x) = ( x θ e −x 2 2θ , for x > 0 0 , otherwise you must now find a good estimator for θ based on your data. hint: if you "rayleigh distribution and mean, mle, etc." you are likely going to confuse yourself and get this problem wrong. i parameterized it differently. • a: find the expected value of the rayleigh distribution, as stated above. hint: let r = x 2 2θ and the manipulate the integral so that it becomes a product of a gamma function and a constant. then use gamma function properties to evaluate the integral. • b: find the method of moments estimator for θ using x1, x2, xn. • c: calculate the bias of the method of moments estimator. • d: find the maximum likelihood estimator for θ using x1, x2, xn.

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