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You repeatedly roll a biased die, where, on any given roll, the probability of each outcome is (pi : i = 1, ..., 6). Let T be the first roll on which the die does not show a 6 and let X be the number shown on roll T. i)  Give the probability distribution of T . ii)  What is the mean of T? [4 marks] [4 marks] iii) Derive the joint probability distribution

You repeatedly roll a biased die, where, on any given roll, the probability of each outcome is (pi : i = 1, ..., 6). Let T be the first roll on which the die does not show a 6 and let X be the number shown on roll T. i)  Give the probability distribution of T . ii)  What is the mean of T? [4 marks] [4 marks] iii) Derive the joint probability distribution

A First Course in Probability (10th Edition)
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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You repeatedly roll a biased die, where, on any given roll, the probability of each outcome is (pi : i = 1, ..., 6). Let T be the first roll on which the die does not show a 6 and let X be the number shown on roll T.

  1. i)  Give the probability distribution of T .

  2. ii)  What is the mean of T?

[4 marks] [4 marks]

iii) Derive the joint probability distribution of T and X. That is, find P(T = t,X = x) for t ∈ N and x = 1,...,5.

iv) Are X and T independent? Justify your answer.

 

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