5. An integer N is chosen from 1 to 10 uniformly at random. Two random variables are defined: X is 1 plus the remainder on division of N by 3. So e.g. when N = 5, the remainder on division by 3 is 2, so X = 3. Y is [N/3]. So e.g. when N = 5, Y = 2. (a) Find E[X], E[Y] and Var[Y]. (b) Are X and Y independent?
5. An integer N is chosen from 1 to 10 uniformly at random. Two random variables are defined: X is 1 plus the remainder on division of N by 3. So e.g. when N = 5, the remainder on division by 3 is 2, so X = 3. Y is [N/3]. So e.g. when N = 5, Y = 2. (a) Find E[X], E[Y] and Var[Y]. (b) Are X and Y independent?
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 23E
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![5. An integer N is chosen from 1 to 10 uniformly at random.
Two random variables are defined:
X is 1 plus the remainder on division of N by 3. So e.g. when N = 5, the remainder on
division by 3 is 2, so X = 3.
Y is [N/3]. So e.g. when N = 5, Y = 2.
(a) Find E[X], E[Y] and Var[Y].
(b) Are X and Y independent?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9f9c13e2-5c54-4ec3-b4e3-dc49b76d4e30%2Fe61fd21f-6025-4434-aebb-db1ce75d4e34%2Fc5tvmxg_processed.png&w=3840&q=75)
Transcribed Image Text:5. An integer N is chosen from 1 to 10 uniformly at random.
Two random variables are defined:
X is 1 plus the remainder on division of N by 3. So e.g. when N = 5, the remainder on
division by 3 is 2, so X = 3.
Y is [N/3]. So e.g. when N = 5, Y = 2.
(a) Find E[X], E[Y] and Var[Y].
(b) Are X and Y independent?
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