Consider an Exponential random variable X with parameter > 0. Let Y = [X], which means
Question:
So the mass of Y is exactly
PY(y) = P(Y = y) = P(y ≤ X ≤ y + 1).
a. Find an expression for the mass of Y. (Your expression will have A in it;
i.e., just integrate to find the value of P(y ≤ X ≤ y + 1), and then simplify.)
b. Do you recognize the mass of Y? (Yes, you should!) What type of random variable is Y? What are the parameters of Y?
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Related Book For
Introduction to Probability
ISBN: 978-0716771098
1st edition
Authors: Mark Daniel Ward, Ellen Gundlach
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