1) Let X₁, X2, X3, ... Xn be a sequence of independent and identically distributed with the following probability density function 1 f(x; 0)=√√2π =e=1/(x-0) ² if - ∞0 < x < 0 otherwise 0, a) Is f(x; 0) a member of one-parameter regular exponential family? If yes, write down the functions, h(x), c(0), w(0) and t(x). b) Find the maximum likelihood estimator of the parameter 0. c) Find the variance of the maximum likelihood estimator of the parameter 0.

1) Let X₁, X2, X3, ... Xn be a sequence of independent and identically distributed with the following probability density function 1 f(x; 0)=√√2π =e=1/(x-0) ² if - ∞0 < x < 0 otherwise 0, a) Is f(x; 0) a member of one-parameter regular exponential family? If yes, write down the functions, h(x), c(0), w(0) and t(x). b) Find the maximum likelihood estimator of the parameter 0. c) Find the variance of the maximum likelihood estimator of the parameter 0.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter13: Probability And Calculus

Section13.1: Continuous Probability Models

Problem 31E: Show that each function defined as follows is a probability density function on the given interval;...

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