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.

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)

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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Question

* 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.

Expression, rule, or law that gives the relationship between an independent variable and dependent variable. Some important types of functions are injective function, surjective function, polynomial function, and inverse function.

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