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

**Marks:** 4M

**Year:** Dec 2014

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

written 8.3 years ago by | • modified 8.2 years ago |

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

**Marks:** 4M

**Year:** Dec 2014

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written 8.3 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

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

$⟹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 $P(A\cap M)=P(A)P(M|A)$

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