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Given a random variable X with followi P(X = n) = {a(20-n) if 0≤ns otherwise Where a is a constant. Also, let Y be a random variable with th independent. 1. Find the value of the constant a. 2. Find E[X] 3. Find Var[X]

Given a random variable X with followi P(X = n) = {a(20-n) if 0≤ns otherwise Where a is a constant. Also, let Y be a random variable with th independent. 1. Find the value of the constant a. 2. Find E[X] 3. Find Var[X]

A First Course in Probability (10th Edition)
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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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: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]
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
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
Expert Solution
Step 1: We have given that

Probability density function of X is

P(X=n)=a(20−n)  , if 0≤n≤20

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