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

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 32E
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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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