Suppose that Y1, ..., Yn - Poisson (^), A> 0, are independent. Prove by calculation that the common point probability function of the random vector Y = (Y1,..., Yn) has the representation ƒ(y; A) = e¯nλ_At(y) n II ²=1 Y₁!' where t(y) = Σ²²±1 Yi · Continuation of the previous task. Suppose n = 4 and it is observed y = (y1, y2, y3, y4) = (5, 6, 2, 5). Calculate the value of the function A 7→ f (y; λ) at a few points between [0, 7] (even at all integer points) and Draw its graph (of course you can also draw the graph with e.g. R). Note: You can multiply the values of the function by e.g. 10000 to get to a more comfortable order of magnitude. With the help of the picture you have drawn, estimate which value of the parameter A has the highest probability of observations? Note: The function A 7→f (y; A) is often denoted L(^; y) and is called the credibility function of the model.
Suppose that Y1, ..., Yn - Poisson (^), A> 0, are independent. Prove by calculation that the common point probability function of the random vector Y = (Y1,..., Yn) has the representation ƒ(y; A) = e¯nλ_At(y) n II ²=1 Y₁!' where t(y) = Σ²²±1 Yi · Continuation of the previous task. Suppose n = 4 and it is observed y = (y1, y2, y3, y4) = (5, 6, 2, 5). Calculate the value of the function A 7→ f (y; λ) at a few points between [0, 7] (even at all integer points) and Draw its graph (of course you can also draw the graph with e.g. R). Note: You can multiply the values of the function by e.g. 10000 to get to a more comfortable order of magnitude. With the help of the picture you have drawn, estimate which value of the parameter A has the highest probability of observations? Note: The function A 7→f (y; A) is often denoted L(^; y) and is called the credibility function of the model.
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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Show step by step calculation. Please calculate everything and give the final answer and also do the graphic. (No explanation needed)
![Suppose that Y1, ..., Yn - Poisson (^), A> 0, are independent. Prove by
calculation that the common point probability function of the random vector Y =
(Y1,..., Yn) has the representation
ƒ(y; A) = e¯nλ_At(y)
n
II ²=1 Y₁!'
where t(y) = Σ²²±1 Yi ·
Continuation of the previous task. Suppose n = 4 and it is observed
y = (y1, y2, y3, y4) = (5, 6, 2, 5). Calculate the value of the function A 7→ f (y; λ) at
a few points between [0, 7] (even at all integer points) and Draw its graph (of
course you can also draw the graph with e.g. R). Note: You can multiply the values
of the function by e.g. 10000 to get to a more comfortable order of magnitude. With
the help of the picture you have drawn, estimate which value of the parameter A
has the highest probability of observations? Note: The function A 7→f (y; A) is often
denoted L(^; y) and is called the credibility function of the model.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F20e8e084-a873-4654-9eae-074b3022d2ce%2F849907a3-2b3a-44af-9cdb-a904d7c5f5a7%2Fox2v7a_processed.png&w=3840&q=75)
Transcribed Image Text:Suppose that Y1, ..., Yn - Poisson (^), A> 0, are independent. Prove by
calculation that the common point probability function of the random vector Y =
(Y1,..., Yn) has the representation
ƒ(y; A) = e¯nλ_At(y)
n
II ²=1 Y₁!'
where t(y) = Σ²²±1 Yi ·
Continuation of the previous task. Suppose n = 4 and it is observed
y = (y1, y2, y3, y4) = (5, 6, 2, 5). Calculate the value of the function A 7→ f (y; λ) at
a few points between [0, 7] (even at all integer points) and Draw its graph (of
course you can also draw the graph with e.g. R). Note: You can multiply the values
of the function by e.g. 10000 to get to a more comfortable order of magnitude. With
the help of the picture you have drawn, estimate which value of the parameter A
has the highest probability of observations? Note: The function A 7→f (y; A) is often
denoted L(^; y) and is called the credibility function of the model.
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