Let X and Y denote two discrete random variables taking the values in x and y respectively. The collected data over time is represented in the following stochastic model: ?(? = ?, ? = ?) = ?(?, ?). a) Check that this table describes a valid joint probability mass function. b) Find the marginal probabilities of ?? (3)??? ??(2). c) Find following the probability: (i) ?(? = 2, ? = 2), (ii) ?(? = 2 | ? = 2) , (iii) ?(? ≤ 3) d) Find the mean of X. e) Are the X and Y independent? Explain. Note: Kindly assess the table in the picture attached for more information.
Let X and Y denote two discrete random variables taking the values in x and y respectively. The collected data over time is represented in the following stochastic model: ?(? = ?, ? = ?) = ?(?, ?). a) Check that this table describes a valid joint probability mass function. b) Find the marginal probabilities of ?? (3)??? ??(2). c) Find following the probability: (i) ?(? = 2, ? = 2), (ii) ?(? = 2 | ? = 2) , (iii) ?(? ≤ 3) d) Find the mean of X. e) Are the X and Y independent? Explain. Note: Kindly assess the table in the picture attached for more information.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.CR: Chapter 13 Review
Problem 29CR
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Question 1: Let X and Y denote two discrete random variables taking the values in x and y respectively. The collected data over time is represented in the following stochastic model: ?(? = ?, ? = ?) = ?(?, ?).
a) Check that this table describes a valid joint probability mass
b) Find the marginal probabilities of ?? (3)??? ??(2).
c) Find following the probability: (i) ?(? = 2, ? = 2), (ii) ?(? = 2 | ? = 2) , (iii) ?(? ≤ 3)
d) Find the mean of X.
e) Are the X and Y independent? Explain.
Note: Kindly assess the table in the picture attached for more information.
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