When 4 dice are tossed, let the random variable X represent the number of obtained “ones” and let the random variable Y represent the number of obtained “twos”. (a) Find the joint probability function of X and Y. (b) Find the marginal probability functions of X and Y, and determine whether X and Y are independent random variables.

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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* Please use the table below for Normal Cumulative Distribution 

* please when you use a normal approximation for discrete random variables, please apply (half-unit) continuity correction

 

When 4 dice are tossed, let the random variable X represent the number of obtained “ones”
and let the random variable Y represent the number of obtained “twos”.
(a) Find the joint probability function of X and Y.
(b) Find the marginal probability functions of X and Y, and determine whether X and Y are independent random variables.

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