Solution Found!
Suppose that Y is a random variable that takes on only
Chapter 4, Problem 5E(choose chapter or problem)
Suppose that is a random variable that takes on only integer values
and has distribution function \(F(y)\). Show that the probability function \(p(y)=P(Y=y)\) is given by
\(p(y)=\left\{\begin{array}{ll}
F(1), & y=1, \\
F(y)-F(y-1), & y=2,3, \ldots .
\end{array}\right.
\)
Equation Transcription:
Text Transcription:
F(y)
p(y)=P(Y=y)
p(y)=F(1),
y=1
p(y)=F(1)-F(y-1)
y=2
Questions & Answers
QUESTION:
Suppose that is a random variable that takes on only integer values
and has distribution function \(F(y)\). Show that the probability function \(p(y)=P(Y=y)\) is given by
\(p(y)=\left\{\begin{array}{ll}
F(1), & y=1, \\
F(y)-F(y-1), & y=2,3, \ldots .
\end{array}\right.
\)
Equation Transcription:
Text Transcription:
F(y)
p(y)=P(Y=y)
p(y)=F(1),
y=1
p(y)=F(1)-F(y-1)
y=2
ANSWER:
Solution:
Step 1 of 2:
Let Y is a random variable that takes on only integer values 1, 2, 3, … and has the distribution function F(y)
The claim is to show that the probability function p(y) = P(Y = y)
