Grinstead-Snell-Probability · Problem 4.1.48

Conditional Probability

Mathematics · conditional-distribution-function

Problem

Let

\Omega

be the sample space of an experiment. Let

E

be an event with

P(E) > 0

and define

m_E(\omega)

m_E(\omega) = m(\omega|E)

. Prove that

m_E(\omega)

is a distribution function on

E

, that is, that

m_E(\omega) \geq 0

and that

\sum_{\omega \in \Omega} m_E(\omega) = 1

. The function

m_E

is called the conditional distribution given

E