Let X1, X2,..., Xn be a random sample from a distribution with a pdf ax. ae ';x > 0 f(x) 0, elsewhere. (a) Find the method of moments estimator for a. (b) Find the MLE for a. (c) Find the MLE for the variance of the distribution.
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- If X is a uniformly distributed random varibale with a=8 and b=13, then Calculate the mean and variance of X? Round to three decimal placesSuppose X1, ..., Xn have been randomly sampled from a normal distribution with mean 0 and unknown variance sigma^2, and let U = c * i=1 -> n summation (X_ i)^2 , where c is a constant. Find the value of c that minimises the Mean Squared Error (MSE)Let X1, ..., Xn be a sample from an exponential population with parameter λ.(a) Find the maximum likelihood estimator for λ. (b) Is the estimator unbiased?(c) Is the estimator consistent?
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