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State and explain: i. Independent Events ii. Joint and conditional probabilities of events

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

Marks: 4M

Year: Dec 2014

1 Answer
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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(AB)(PB)=P(A)

P(AB) 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(AM)P(M)>0

The above definition gives,

P(AM)=P(AM)=P(M)P(A/M) or P(AM)=P(A)P(M|A)

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