Let X Beta(a, B) andY Beta distribution pdf: fx (x) = caª-1(1 – x)8–1 for x E (0, 1) and parameters a > 0, ß > 0, T(a + 8) Г(а)Г(3) where c is a normalizing constant equal to (Recall that I(z +1) = zr(2) 2(2 — 1) Г(г — 1) %3D..) = Question part 2: What is E[X³]?
Let X Beta(a, B) andY Beta distribution pdf: fx (x) = caª-1(1 – x)8–1 for x E (0, 1) and parameters a > 0, ß > 0, T(a + 8) Г(а)Г(3) where c is a normalizing constant equal to (Recall that I(z +1) = zr(2) 2(2 — 1) Г(г — 1) %3D..) = Question part 2: What is E[X³]?
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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![1
Beta(a, B) and Y :
X
Let X ~
Beta distribution pdf:
fx (x) = caº-1(1 – x)8–1
for x E (0, 1) and parameters a > 0, ß > 0,
T(a + B)
where c is a normalizing constant equal to
T(a)r(B)
(Recall that I'(z + 1) = zr(z) = z(z – 1)T(z – 1) =...)
-
Question part 2:
What is E[X³]?
hint: use the kernel trick.
O We do not have enough information to answer this question.
( α +2) (α + 1)α
(a + B+ 2)(a + ß+ 1)(a + B)
(a + B)3
Ο r(α+β+ 3)
r(α+ 3)Γ(β)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F419820c1-e9cd-469e-aa42-67c8a6edd9ca%2F1c737938-81ed-40b0-97c6-d4dc3dfeaf4a%2Fclbppx_processed.png&w=3840&q=75)
Transcribed Image Text:1
Beta(a, B) and Y :
X
Let X ~
Beta distribution pdf:
fx (x) = caº-1(1 – x)8–1
for x E (0, 1) and parameters a > 0, ß > 0,
T(a + B)
where c is a normalizing constant equal to
T(a)r(B)
(Recall that I'(z + 1) = zr(z) = z(z – 1)T(z – 1) =...)
-
Question part 2:
What is E[X³]?
hint: use the kernel trick.
O We do not have enough information to answer this question.
( α +2) (α + 1)α
(a + B+ 2)(a + ß+ 1)(a + B)
(a + B)3
Ο r(α+β+ 3)
r(α+ 3)Γ(β)
![„part 4:
what is Cov[X,Y]? (again, assume that a > 1)
° 2-2,() -0
a + B)
a + B
O, since they are independent
01-()
a + B – 1
( α-1) (α + β)
a + B
- 1
0, since X and Y are functions of each other.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F419820c1-e9cd-469e-aa42-67c8a6edd9ca%2F1c737938-81ed-40b0-97c6-d4dc3dfeaf4a%2Fi1h1lb4_processed.png&w=3840&q=75)
Transcribed Image Text:„part 4:
what is Cov[X,Y]? (again, assume that a > 1)
° 2-2,() -0
a + B)
a + B
O, since they are independent
01-()
a + B – 1
( α-1) (α + β)
a + B
- 1
0, since X and Y are functions of each other.
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