Exercise 9.2 Consider an i.i.d. sample of size n from a N(μ, o2) distributed random variable X. (a) Determine the maximum likelihood estimator for under the assumption that o² = 1. (b) Now determine the maximum likelihood estimator for μ for an arbitrary o².
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- Let X1 and X2 be independent chi-square random variables with r1 and r2 degrees of freedom, respectively. Let Y1=(X1/r1)/(X2/r2) and Y2=X2. (a) Find the joint pdf of Y1 and Y2.the pdf of a random variable x is given by f(x;θ) = θx^θ−1 x ∈ (0,1). find the maximum likelihood estimate of θLet X1, ..., Xn be a sample from a geometric random variable with parameter p.(a) Find the maximum likelihood estimator for p.(b) Is the estimator unbiased?(c) Is the estimator consistent?
- If X is a uniformly distributed random varibale with a=9 and b=16, then Calculate the variance of X? Round to three decimal placesIf X1,X2,...,Xn constitute a random sample of size n from a gamma population with α =2, use the method of maximum likelihood to find a formula for estimating β.Let X be a Gaussian random variable (0,1). Let M = ln(5*X) be a derived random variable. What is E[M]?
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