Use the ideas in the above to investigate whether the sum of two independent geometricly distributed (with parameter 1/41/4) random variables is also geometrically distributed (with a suitable parameter) (you may follow all parts above if you would like).
Solve Question 2, Question 1 is just there to use to answeer question 2.
Question 1
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Write down the
pdf as a table of a random variable X∼Binom(2,.3) and the pdf as a table of a random variable Y∼Binom(1,.4). -
What experiments might you imagine that would lead to consideration of the above?
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Suppose the variables are independent (meaning any
event described using X is independent of any event described using y). Write down a table for the Random Variable Z:=X+Y. -
Use R to simulate the 2 experiments and Z (provide a pdf of the code and result).
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Approximate P(Z≤1) using your simulated data.
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Compare your answer to e) with the information in your table in part c). It should agree, so if it does not, go back and find any error and comment on your process of discovery here.
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Is Z a binomial random variable? (Hint: If it where, how does P(Z=0) depend on pp and how does the length of the table depend on nn and does the binomial distribution with the parameters that Z must have if it were binomial actually agree with the information in your investigations of Z?
Question 2
Use the ideas in the above to investigate whether the sum of two independent geometricly distributed (with parameter 1/41/4) random variables is also geometrically distributed (with a suitable parameter) (you may follow all parts above if you would like).
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