a) Suppose that Y1, . . ., Yn ~ Poisson(\), \ > 0, are independent. Prove by calculation that the common point probability function of the random vector Y = (Y1,..., Yn) has the representation f(y; λ) = e -nλ λt(y) i=1 [I'l²±1 Yi!' where t(y) = Σ²²±1 Yi - i=1 b) 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 à 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.
a) Suppose that Y1, . . ., Yn ~ Poisson(\), \ > 0, are independent. Prove by calculation that the common point probability function of the random vector Y = (Y1,..., Yn) has the representation f(y; λ) = e -nλ λt(y) i=1 [I'l²±1 Yi!' where t(y) = Σ²²±1 Yi - i=1 b) 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 à 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.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 32E
Related questions
Question
![a) Suppose that Y1, . . ., Yn ~ Poisson(\), \ > 0, are independent. Prove by
calculation that the common point probability function of the random vector Y =
(Y1,..., Yn) has the representation
f(y; λ) = e
-nλ
λt(y)
i=1
[I'l²±1 Yi!'
where t(y) = Σ²²±1 Yi -
i=1
b) 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 à 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%2Fa7e2cf29-ffd8-48c0-88bf-7bb56671ed3c%2F8p3o4zv_processed.png&w=3840&q=75)
Transcribed Image Text:a) Suppose that Y1, . . ., Yn ~ Poisson(\), \ > 0, are independent. Prove by
calculation that the common point probability function of the random vector Y =
(Y1,..., Yn) has the representation
f(y; λ) = e
-nλ
λt(y)
i=1
[I'l²±1 Yi!'
where t(y) = Σ²²±1 Yi -
i=1
b) 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 à 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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