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SC-215 Probability Theory
Instructor: Prof. Jaideep Mulherkar
Topics for PhD comprehensive (Probability and Statistics)
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Axiomatic probability, counting, Inclusion-Exclusion principle
Conditional probability and Independence
Random Variables
o Distribution function,
o Probability mass and density function
o Expectation, properties of expectation.
Some probability distributions
o Binomial, Poisson, Geometric (Discrete)
o Uniform, Normal, Exponential ( Continuous)
Joint distribution of random variables
Law of large numbers, Central Limit Theorem
Books
 A first course in probability By Sheldon Ross, Sixth edition.
1. If 5 married couples are seated at random around a round table, what is the
probability that no wife sits next to her husband. (Hint: Use Inclusion-Exclusion)
2. A and B alternate rolling a pair of dice, stopping either when A rolls the sum of 9
or when B rolls the sum 6. Assuming that A rolls first, find the probability that the
final roll is made by A.
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4. One has 100 lightbulbs whose lifetimes are independent exponential random
variables with mean 5 hrs and variance 25 hrs. If the bulbs are used one at a time,
with a failed bulb being replaced immediately by a new one, what is the
probability that there is still a working bulb after 525 hrs ? (Hint: Central Limit
threorem)