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F(1), p(y) - y - 1, F(Y) - F(y - 1), y - 2, 3, ...

F(1), p(y) - y - 1, F(Y) - F(y - 1), y - 2, 3, ...

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Suppose that Y is a random variable that takes on only integer values 1, 2, ... and has distribution function F(y). Show that the probability function p(y) = P(Y = y) is given by the following. F(1), p(y) = y = 1, Fly) - F(y - 1), y = 2, 3, ... Since Y takes on only non-negative integer values, when y > 1 we know P(Y = y) = p(y) can be written as p(y) = --Select- v. By definition F(y) = P(Y?y). And so p(y) = Select-- v. Finally, since Y 2 1 we know p(1) = --Select-- v. And so, we know p(1) = Select--
Transcribed Image Text:Suppose that Y is a random variable that takes on only integer values 1, 2, ... and has distribution function F(y). Show that the probability function p(y) = P(Y = y) is given by the following. F(1), p(y) = y = 1, Fly) - F(y - 1), y = 2, 3, ... Since Y takes on only non-negative integer values, when y > 1 we know P(Y = y) = p(y) can be written as p(y) = --Select- v. By definition F(y) = P(Y?y). And so p(y) = Select-- v. Finally, since Y 2 1 we know p(1) = --Select-- v. And so, we know p(1) = Select--
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