Question part 3: What is E[Y]? Assume that a > 1. L triel
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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Transcribed Image Text:1
Let X - Beta(a, B) and Y =
Beta distribution pdf:
fx (x) = cx"-1(1 – x)³-1 for x € (0, 1) and parameters a > 0, B > 0,
Γ (α + β)
where c is a normalizing constant equal to
Г(а)Г(8)
(Recall that I'(z + 1) = zT(z) = z(z – 1)r(z – 1) =...)
Question part 3:
What is EY? Assume that a > 1.
hint: again, use the kernel trick.
a + B
a – B
a + B
1
1
1
-1
+B
a + B
We do not have enough information to answer this question.
![1
Let X - Beta(a, B) and Y =
Beta distribution pdf:
fx (x) = cx"-1(1 – x)B-1 for x E (0, 1) and parameters a > 0, B > 0,
T(a + B)
where c is a normalizing constant equal to
I(a)r(8)
Recall that I'(z + 1) = zT(z) = z(z – 1)T(z – 1) =
=...
Question part 1:
E X = . What is E[X²]?
a+B*
hint: using the kernel trick (figuring out a new normalizing constant) will probably be
faster than looking up the variance and doing the necessary algebra. Consolidate your
x terms and recognize the new Beta distribution's parameters to figure out its
normalizing constant.
aß
(a + B)2 (a + B+ 1)
a?
(a+ B)2
We do not have enough information to answer this question.
(a +1)a
(a +B+1)(a + B)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe5f558a7-14fc-4024-84d6-4debb1adc6f6%2F58e9fed2-c491-4033-9c73-e013a4b35a55%2Flp3uite_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1
Let X - Beta(a, B) and Y =
Beta distribution pdf:
fx (x) = cx"-1(1 – x)B-1 for x E (0, 1) and parameters a > 0, B > 0,
T(a + B)
where c is a normalizing constant equal to
I(a)r(8)
Recall that I'(z + 1) = zT(z) = z(z – 1)T(z – 1) =
=...
Question part 1:
E X = . What is E[X²]?
a+B*
hint: using the kernel trick (figuring out a new normalizing constant) will probably be
faster than looking up the variance and doing the necessary algebra. Consolidate your
x terms and recognize the new Beta distribution's parameters to figure out its
normalizing constant.
aß
(a + B)2 (a + B+ 1)
a?
(a+ B)2
We do not have enough information to answer this question.
(a +1)a
(a +B+1)(a + B)
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