c) Mr Ledwaba from Department of Health assumed that a random variable X is normal with mean 2 and standard deviation 3 and that random variable Y is normal with mean 0 and standard deviation 4. Suppose that X and Y are independent, use an appropriate method to determine his probability distribution of the random variable X + Y.
c) Mr Ledwaba from Department of Health assumed that a random variable X is normal with mean 2 and standard deviation 3 and that random variable Y is normal with mean 0 and standard deviation 4. Suppose that X and Y are independent, use an appropriate method to determine his probability distribution of the random variable X + Y.
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 11ECP: A manufacturer has determined that a machine averages one faulty unit for every 500 it produces....
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![c) Mr Ledwaba from Department of Health assumed that a random variable X is normal with
mean 2 and standard deviation 3 and that random variable Y is normal with mean 0 and
standard deviation 4. Suppose that X and Y are independent, use an appropriate method
to determine his probability distribution of the random variable X + 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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc7f442cf-541d-4442-b6c8-0606c8499d0b%2F3851bbf2-5ad7-40b1-bf57-13d4c8737b43%2Far9zo3_processed.jpeg&w=3840&q=75)
Transcribed Image Text:c) Mr Ledwaba from Department of Health assumed that a random variable X is normal with
mean 2 and standard deviation 3 and that random variable Y is normal with mean 0 and
standard deviation 4. Suppose that X and Y are independent, use an appropriate method
to determine his probability distribution of the random variable X + 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
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