Probability, Stochastic Processes, and Statistics: Course Syllabus, Assignments of Mathematics

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19I401 - PROBABILITY, STOCHASTIC PROCESSES AND STATISTICS

19I401 - PROBABILITY, STOCHASTIC PROCESSES AND STATISTICS

Chapter 1: PROBABILITY AND DISCRETE RANDOM VARIABLES Chapter 2: CONTINUOUS RANDOM VARIABLES Chapter 3: PAIRS OF RANDOM VARIABLES Chapter 4: STOCHASTIC PROCESSES Chapter 5: STATISTICAL INFERENCE

Week - 2

Probability :

• Axiomatic approach to probability
• Baye’s theorem

Text Books:

T1. Roy D Yates and David J Goodman, “Probability and Stochastic Processes - A

friendly Introduction for Electrical and Computer Engineers”, Wiley India, New

Delhi, 2014.

T2. Ronald E. Walpole, Raymond H Myers, Sharon L Myers and Keying Ye,

“Probability and Statistics for Engineers and Scientists”, Pearsons, New Delhi, 2016

General multiplication rule of probability Special product rule of probability: Two events A and B are independent events if and only if P ( A ∩ B ) = P ( A ) ・ P ( B )

CONDITIONAL PROBABILITY

CONDITIONAL PROBABILITY

BAY’S THEOREM

Rule of total probability

Bay’s Theorem

BAY’S THEOREM

Problem – Bay’s Theorem

 If the conditional probability of B given A is equal to the unconditional probability

of B as P(B|A)=P(B) then, A and B are said to be independent

 This is equivalent to P(A|B)=P(A) or P(A∩B )=P(B)P(A|B)=P(B)*P(A)

 P(A∩B )=P(A)*P(B)

 P(A|B)=P(A)

 P(B|A)=P(B)

 If any of these 3 conditions holds, then A & B are independent.

 If any of these 3 conditions does not hold, then A & B are dependent.

INDEPENDENT EVENTS