Suppose X1,...,Xn are iid with PDF f(x | θ) = 2x/θ2, 0 < x < θ. (a) Write out the joint PDF f(x | θ), and write the likelihood function L(θ | x). (b) Find the MLE for θ. (c) Find the MLE for the median of the distribution.

Suppose X1,...,Xn are iid with PDF f(x | θ) = 2x/θ2, 0 < x < θ. (a) Write out the joint PDF f(x | θ), and write the likelihood function L(θ | x). (b) Find the MLE for θ. (c) Find the MLE for the median of the distribution.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

Suppose X₁,...,X_n are iid with PDF f(x | θ) = 2x/θ², 0 < x < θ.

(a) Write out the joint PDF f(x | θ), and write the likelihood function L(θ | x).

(b) Find the MLE for θ.

(c) Find the MLE for the median of the distribution.

Expression, rule, or law that gives the relationship between an independent variable and dependent variable. Some important types of functions are injective function, surjective function, polynomial function, and inverse function.

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Step 2: Write out the joint PDF f(x | θ), and write the likelihood function L(θ | x).

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Step 3: Determine the MLE for θ

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Step 4: Determine the MLE for the median of the distribution

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