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Let X₁, X₂ be 2 mutually independent discrete random variables. The first variable X₁ can be a whole number from 1 to 5. Its distribution function is 6 - i m₁ (i) 15 The second variable X₂ can be a whole number from 1 to 6. It has a uniform distribution. First, find the exact values (using fractions) of P(X₁ = 3) = 1/5 : P(X₂ = 5) = 1/6 P(X₁ = 3 and 3 and X₂ = 5) = 1/30 X₂ # Let Y denote the maximum of the X¿'s. Find the probability that Y = 1: P(Y = 1) = 1 Find the probability that Y = 2, P(Y= 2) = 2/45 Hint: Use cases based on what X₁ and X₂ are.

Let X₁, X₂ be 2 mutually independent discrete random variables. The first variable X₁ can be a whole number from 1 to 5. Its distribution function is 6 - i m₁ (i) 15 The second variable X₂ can be a whole number from 1 to 6. It has a uniform distribution. First, find the exact values (using fractions) of P(X₁ = 3) = 1/5 : P(X₂ = 5) = 1/6 P(X₁ = 3 and 3 and X₂ = 5) = 1/30 X₂ # Let Y denote the maximum of the X¿'s. Find the probability that Y = 1: P(Y = 1) = 1 Find the probability that Y = 2, P(Y= 2) = 2/45 Hint: Use cases based on what X₁ and X₂ are.

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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Let X₁, X₂ be 2 mutually independent discrete random variables. The first variable X₁ can be a whole number from 1 to 5. Its distribution function is 6 - i m₁ (i) 15 The second variable X₂ can be a whole number from 1 to 6. It has a uniform distribution. First, find the exact values (using fractions) of P(X₁ = 3) = 1/5 : P(X₂ = 5) = 1/6 P(X₁ = 3 and 3 and X₂ = 5) = 1/30 X₂ # Let Y denote the maximum of the X¿'s. Find the probability that Y = 1: P(Y = 1) = 1 Find the probability that Y = 2, P(Y= 2) = 2/45 Hint: Use cases based on what X₁ and X₂ are.
Transcribed Image Text:Let X₁, X₂ be 2 mutually independent discrete random variables. The first variable X₁ can be a whole number from 1 to 5. Its distribution function is 6 - i m₁ (i) 15 The second variable X₂ can be a whole number from 1 to 6. It has a uniform distribution. First, find the exact values (using fractions) of P(X₁ = 3) = 1/5 : P(X₂ = 5) = 1/6 P(X₁ = 3 and 3 and X₂ = 5) = 1/30 X₂ # Let Y denote the maximum of the X¿'s. Find the probability that Y = 1: P(Y = 1) = 1 Find the probability that Y = 2, P(Y= 2) = 2/45 Hint: Use cases based on what X₁ and X₂ are.
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