Given a random variable X with following distribution: Ja(20-n) if 0≤ n ≤ 20 0 otherwise P(X = n) = Where a is a constant. Also, let Y be a random variable with the same distribution as X. Y and X are independent. 1. Find the value of the constant a. 2. Find E[X] 3. Find Var[X] 4. Find P[X - Y = 0] 5. Find E[X - Y] 6. Find Var[X − Y] -
Given a random variable X with following distribution: Ja(20-n) if 0≤ n ≤ 20 0 otherwise P(X = n) = Where a is a constant. Also, let Y be a random variable with the same distribution as X. Y and X are independent. 1. Find the value of the constant a. 2. Find E[X] 3. Find Var[X] 4. Find P[X - Y = 0] 5. Find E[X - Y] 6. Find Var[X − Y] -
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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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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![Given a random variable X with following distribution:
P(X = n) = {a(20-n) if 0≤n≤ 20
"
otherwise
Where a is a constant.
Also, let y be a random variable with the same distribution as X. Y and X are
independent.
1. Find the value of the constant a.
2. Find E[X]
3. Find Var[X]
4. Find P[X - Y = 0]
5. Find E[X-Y]
6. Find Var[X-Y]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F892e817a-9b32-4eeb-b8fc-5dd7ffde6479%2Facf99f50-500c-4b7b-928c-f86bb6d45931%2Fyf4sjpq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Given a random variable X with following distribution:
P(X = n) = {a(20-n) if 0≤n≤ 20
"
otherwise
Where a is a constant.
Also, let y be a random variable with the same distribution as X. Y and X are
independent.
1. Find the value of the constant a.
2. Find E[X]
3. Find Var[X]
4. Find P[X - Y = 0]
5. Find E[X-Y]
6. Find Var[X-Y]
Transcribed Image Text:You may use the following sums:
K
k=1
k =
K(K + 1)
2
;
K
Σκε
k=1
=
K(K + 1)(2K + 1)
6
;
K
Σ
k=1
k3
=
K2(K + 1)2
4
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