written 8.8 years ago by | • modified 8.8 years ago |
Mumbai University > Electronics and Telecommunication > Sem5 > Random Signal Analysis
Marks: 4M
Year: Dec 2014
written 8.8 years ago by | • modified 8.8 years ago |
Mumbai University > Electronics and Telecommunication > Sem5 > Random Signal Analysis
Marks: 4M
Year: Dec 2014
written 8.8 years ago by |
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
P(A∩B)(PB)=P(A)
⟹P(A∩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)=P(A∩M)P(M)>0
The above definition gives,
P(A∩M)=P(AM)=P(M)P(A/M) or P(A∩M)=P(A)P(M|A)