Mrs Legodi, a registered student at the University of Limpopo, tossed a fair coin three times. She decided to let X to be a random variable that takes the value 1 if the outcome of a toss is a head and the value 0 otherwise. She also defined Y to be a random variable of the total number of heads in the three tosses. i) What will be her joint probability mass function (PMF) of X and Y? ii) Find the P(X = 0, y = 1]. iii) Determine the marginal PMF of X. iv) Show whether or not X and Y independent without using marginal PMFs of X and Y.

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
Question

12.THEORY OF DISTRIBUTIONS

Mrs Legodi, a registered student at the University of Limpopo, tossed a fair coin three
times. She decided to let X to be a random variable that takes the value 1 if the outcome
of a toss is a head and the value 0 otherwise. She also defined Y to be a random variable
of the total number of heads in the three tosses.
i) What will be her joint probability mass function (PMF) of X and Y?
ii) Find the P(X = 0, y = 1].
iii) Determine the marginal PMF of X.
iv) Show whether or not X and Y independent without using marginal PMFs of X and Y.
Transcribed Image Text:Mrs Legodi, a registered student at the University of Limpopo, tossed a fair coin three times. She decided to let X to be a random variable that takes the value 1 if the outcome of a toss is a head and the value 0 otherwise. She also defined Y to be a random variable of the total number of heads in the three tosses. i) What will be her joint probability mass function (PMF) of X and Y? ii) Find the P(X = 0, y = 1]. iii) Determine the marginal PMF of X. iv) Show whether or not X and Y independent without using marginal PMFs of X and Y.
Expert Solution
steps

Step by step

Solved in 5 steps

Blurred answer
Similar questions
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman