we are given independent random variables X and Y distrubuted: X ∼ poisson(θ) , Y ∼ poisson(2θ), and observations x = 3 and y = 5. Show that the expression for the log-likehood function is given by: l(θ)=[5ln(2)−ln(3!)−ln(5!)]+8lnθ−3θ. Make a rough sketch of l(θ) with valeus from θ [0,10]. For which values of θ does l(θ) reach maximum. Estimate the likelihood maximation estimate θ* for the observed values x= 3 and y= 5

we are given independent random variables X and Y distrubuted: X ∼ poisson(θ) , Y ∼ poisson(2θ), and observations x = 3 and y = 5. Show that the expression for the log-likehood function is given by: l(θ)=[5ln(2)−ln(3!)−ln(5!)]+8lnθ−3θ. Make a rough sketch of l(θ) with valeus from θ [0,10]. For which values of θ does l(θ) reach maximum. Estimate the likelihood maximation estimate θ* for the observed values x= 3 and y= 5

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.6: Permutations

Problem 12E

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Question

we are given independent random variables X and Y distrubuted: X ∼ poisson(θ) , Y ∼ poisson(2θ), and observations x = 3 and y = 5.
Show that the expression for the log-likehood function is given by:
l(θ)=[5ln(2)−ln(3!)−ln(5!)]+8lnθ−3θ.
Make a rough sketch of l(θ) with valeus from θ [0,10]. For which values of θ does l(θ) reach maximum.

Estimate the likelihood maximation estimate θ^* for the observed values x= 3 and y= 5

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.

Expert Solution