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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 sketch of l(θ) for θ ∈ [0, 10]. for which value of θ does l(θ) reach its maximum?

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 sketch of l(θ) for θ ∈ [0, 10]. for which value of θ does l(θ) reach its maximum?

College Algebra
College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter6: Exponential And Logarithmic Functions
Section6.8: Fitting Exponential Models To Data
Problem 3TI: Table 6 shows the population, in thousands, of harbor seals in the Wadden Sea over the years 1997 to...
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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 sketch of l(θ) for θ ∈ [0, 10]. for which value of θ does l(θ) reach its maximum?

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