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.
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.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter12: Probability
Section12.CR: Chapter 12 Review
Problem 84CR
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![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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F98045eb8-67c9-4c5f-b511-4afdd76e7951%2Ffc3061c2-523f-48ef-9eb6-93ebd3b0c291%2Fb2oqsj_processed.jpeg&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.
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