4. Let X and Y be independent random variables with gamma distributions, r(3,2) and I'(4,2), respectively. The moment generating function of X and Y are *(1-2)' (1) and ().<. respectively. a) b) c) Calculate E(3X + 2Y+1). Calculate Var (3X + 2Y+1). Obtain the distribution of W = X+Y. (1)
4. Let X and Y be independent random variables with gamma distributions, r(3,2) and I'(4,2), respectively. The moment generating function of X and Y are *(1-2)' (1) and ().<. respectively. a) b) c) Calculate E(3X + 2Y+1). Calculate Var (3X + 2Y+1). Obtain the distribution of W = X+Y. (1)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Question
![4.
Let X and Y be independent random variables with gamma distributions,
r(3,2) and I'(4,2), respectively. The moment generating function of X and
Y are
• (1-2₁)
a)
b)
c)
d)
and
¹ (1-2)* · · </
Calculate E(3X + 2Y+1).
Calculate Var (3X + 2Y + 1).
Compute E
, respectively.
Obtain the distribution of W = X+Y.
(+).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F60abd4de-ba2d-4a53-b8fc-e1d2e0799cec%2F6cdb4fea-012f-47b0-a864-37813ab49005%2Fieckk8u_processed.jpeg&w=3840&q=75)
Transcribed Image Text:4.
Let X and Y be independent random variables with gamma distributions,
r(3,2) and I'(4,2), respectively. The moment generating function of X and
Y are
• (1-2₁)
a)
b)
c)
d)
and
¹ (1-2)* · · </
Calculate E(3X + 2Y+1).
Calculate Var (3X + 2Y + 1).
Compute E
, respectively.
Obtain the distribution of W = X+Y.
(+).
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