Let (x1, x2, · · · , xn) be i.i.d. samples of a random variable X with probability density function fX(x) = λxe−λx^(2)/2 for x ≥ 0. Find the maximum likelihood estimator of λ.  Steps: Find likelihood function Find log likelihood Find derivate Equate to 0 Find 2nd derivative and proof its < 0 to proof it's maximum likelihood

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.
Chapter9: Multivariable Calculus
Section9.1: Functions Of Several Variables
Problem 34E: The following table provides values of the function f(x,y). However, because of potential; errors in...
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Let (x1, x2, · · · , xn) be i.i.d. samples of a random variable X with probability density function fX(x) = λxe−λx^(2)/2 for x ≥ 0. Find the maximum likelihood estimator of λ. 

Steps:
Find likelihood function

Find log likelihood

Find derivate

Equate to 0

Find 2nd derivative and proof its < 0 to proof it's maximum likelihood

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