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

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19I401 -

PROBABILITY, STOCHASTIC PROCESSES AND STATISTI

CS

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

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

Suppose traffic engineers have coordinated the timing of two traffic lights to encourage a run of

green lights. In particular, the timing was designed so that with probability 0. 8 a driver will find the

second light to have the same color as the first. Assuming the first light is equally likely to be red or

green, what is the probability P [ G 2] that the second light is green? Also, what is P [ W ], the

probability that you wait for at least one light? Lastly, what is P [ G 1| R 2], the conditional probability

of a green first light given a red second light?

Consider the game of Three. You shuffle a deck of three cards: ace, 2, 3. With the ace worth 1 point, you draw

cards until your total is 3 or more. You win if your total is 3. What is P [ W ], the probability that you win?

Consider the game of Three. You shuffle a deck of three cards: ace, 2, 3. With the ace worth 1 point, you draw

cards until your total is 3 or more. You win if your total is 3. What is P [ W ], the probability that you win?

Reliability Problems Independent trials can also be used to describe reliability problems in which we would like to calculate the probability that a particular operation succeeds. The operation consists of n components and each component succeeds with probability p , independent of any other component. Let Wi denote the event that component i succeeds. Components in series****. The operation succeeds if all of its components succeed. The complete operation fails if any component program fails. Whenever the operation consists of k components in series, we need all k components to succeed in order to have a successful operation. The probability that the operation succeeds is P [ W ] = P [ W 1 W 2 · · · Wn ] = p × p ×· · ·× p = pn Components in parallel****. The operation succeeds if any component works. This operation occurs when we introduce redundancy to promote reliability. In a redundant system, such as a space shuttle, there are n computers on board so that the shuttle can continue to function as long as at least one computer operates successfully. If the components are in parallel, the operation fails when all elements fail, so we have

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