Suppose you have a fair four sided dice showing {1,2,3,4}. You roll the dice and then continues to roll the dice until it shows a number that is less or the same as the first roll. Let X be the value of the dice on the first roll and let N be the number of rolls that is made after the first roll. a. Determine if X and N is independent. b. Determine the probability P(N>1) c. Determine the joint mass function p(x,n)=P(X=x, N=n) of vector (X, N)

Suppose you have a fair four sided dice showing {1,2,3,4}. You roll the dice and then continues to roll the dice until it shows a number that is less or the same as the first roll. Let X be the value of the dice on the first roll and let N be the number of rolls that is made after the first roll. a. Determine if X and N is independent. b. Determine the probability P(N>1) c. Determine the joint mass function p(x,n)=P(X=x, N=n) of vector (X, N)

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

a. Determine if X and N is independent.

b. Determine the probability P(N>1)

c. Determine the joint mass function p(x,n)=P(X=x, N=n) of vector (X, N)

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