Mumbai University > Electronics and Telecommunication > Sem5 > Random Signal Analysis

Marks: 4M

Year: Dec 2014

i. Independent Events

Two events A and B are said to be independent if the occurrence of one does not affect the probability of occurrence of the other. That is, if A and B are independent, then we should have,

P(A|B) =P(A) (and) P(B|A) =P(B)

From the definition of conditional probability, this means

$\frac{P(A\cap B)}{(P{B})}=P(A)$

$⟹P(A\cap B) $ is often written as P(AB)

ii. Joint and conditional probabilities of events

The Conditional Probability of an event A assuming or given that another event M has occurred, is denoted by defined as:

$P(A/M)=\frac{P(A\cap M)}{P(M)}$>0

The above definition gives,

$P(A\cap M)=P(AM)=P(M)P(A/M)$ or $P(A\cap M)=P(A)P(M|A)$