a random variable that takes the value the value 0 otherwise. She also defined Y to be a rando heads in the three tosses. mt probability mass function (PMF) of X and Y? = 1]. ginal PMF of X. ot X and Y independent without using marginal PMFs of ₂ have the joint probability density function defined as f(x₁, x₂) = { 0, (Wx₁x₂, 0≤x₂ ≤ 1, 0≤x₂ ≤1 elsewhere makes ƒ(x₁, x₂) a probability density function. distribution function for X₁ and X₂.
a random variable that takes the value the value 0 otherwise. She also defined Y to be a rando heads in the three tosses. mt probability mass function (PMF) of X and Y? = 1]. ginal PMF of X. ot X and Y independent without using marginal PMFs of ₂ have the joint probability density function defined as f(x₁, x₂) = { 0, (Wx₁x₂, 0≤x₂ ≤ 1, 0≤x₂ ≤1 elsewhere makes ƒ(x₁, x₂) a probability density function. distribution function for X₁ and X₂.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![a) 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
b) Suppose that X₁ and X₂ have the joint probability density function defined as
f(x₁, x₂) = {Wx₁x2,
(Wx₁x₂, 0≤x₁ ≤ 1,
0 ≤ x₂ ≤ 1
elsewhere
Find:
i) the value of w that makes f(x₁, x₂) a probability density function.
ii) the joint cumulative distribution function for X₁ and X₂.
iii) P (X₂ ≤| X₂ ≤ =).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbc219a71-a3f3-49e8-b112-638d327202a9%2F0f088fe1-4c85-406f-a1e6-61e686fbf14e%2Fnekvshr_processed.png&w=3840&q=75)
Transcribed Image Text:a) 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
b) Suppose that X₁ and X₂ have the joint probability density function defined as
f(x₁, x₂) = {Wx₁x2,
(Wx₁x₂, 0≤x₁ ≤ 1,
0 ≤ x₂ ≤ 1
elsewhere
Find:
i) the value of w that makes f(x₁, x₂) a probability density function.
ii) the joint cumulative distribution function for X₁ and X₂.
iii) P (X₂ ≤| X₂ ≤ =).
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