Question

1. Suppose that X_1, ..., X_n is an iid random sample from a distribution with pdf f(x;sigma) = frac{1}{2sigma} e^{-|x|/sigma}, -infty < x < infty, ; sigma > 0 (a) Find the method of moments estimator (MME) of sigma. (b) Find the maximum likelihood estimator (MLE) of sigma. (c) Use the central limit theorem to find the large-sample asymptotic distribution of the MLE in part (b). (d) Suppose 10 independent observations were taken from the given distribution: (0.5, -0.8, 2.2, -1.6, 2.0, -2.8, 1.5, -0.9, 2.5, -1.8). What is the numerical value of the MLE? What is the numerical value of the estimated standard deviation (standard error) of the MLE?

          1. Suppose that X_1, ..., X_n is an iid random sample from a distribution with pdf

    f(x;sigma) = frac{1}{2sigma} e^{-|x|/sigma},
    -infty < x < infty, ; sigma > 0

(a) Find the method of moments estimator (MME) of sigma.
(b) Find the maximum likelihood estimator (MLE) of sigma.
(c) Use the central limit theorem to find the large-sample asymptotic distribution of the MLE in part (b).
(d) Suppose 10 independent observations were taken from the given distribution: (0.5, -0.8, 2.2, -1.6, 2.0, -2.8, 1.5, -0.9, 2.5, -1.8). What is the numerical value of the MLE? What is the numerical value of the estimated standard deviation (standard error) of the MLE?

$1. Suppose that X1, ..., Xn is an iid random sample from a distribution with pdf f(x;sigma) = frac12sigma e^-|x|/sigma, -infty < x < infty, ; sigma > 0 (a) Find the method of moments estimator (MME) of sigma. (b) Find the maximum likelihood estimator (MLE) of sigma. (c) Use the central limit theorem to find the large-sample asymptotic distribution of the MLE in part (b). (d) Suppose 10 independent observations were taken from the given distribution: (0.5, -0.8, 2.2, -1.6, 2.0, -2.8, 1.5, -0.9, 2.5, -1.8). What is the numerical value of the MLE? What is the numerical value of the estimated standard deviation (standard error) of the MLE?$

Added by Sharon J.

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