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Day  1 2  4 Date Contents Slides Assignments Sep 14 Introduction to probability- simple problems- Rolling a die n times and find the probability of getting at least one six,  probability of forming two men and two women out of four people Lecture Notes - Best one Sep 17 Class Test- 5 Questions: Time-15 minutes Problems 1. 3 men and 3 women are to be seated (i) In a row of chairs (ii) Around a table. What is the probability that all women are seated together in both cases? 2. Divide 52 cards into 4 sets of 13. What is the probability that each set has an Ace? Answers in different methods. 3. Roll a die 12 times- probability that each digit appears exactly twice Question Paper-Test1 3 Sep 18 Probability Space- pairwise disjoint events  x^2+y^2 < 1 -to find probability of an area in this circular portion Problems:  1)In a class there are 9 students and each of them buy a gift and distribute randomly. What is the probability that i) A particular student gets back his/her own gift. ii)Any of the student get back his/her gift. 2) Birthday problem 3) Coupon collector problem Conditional Probability Problem: Two fair blind-folded coins is tossed. Given that atleast one head is tossed. What is the probability that both tosses are heads? First Bayes' formula- Problem: Flip a fair coin. If a head is comes out, then a dice is rolled. If a tail comes out, two dice are rolled. Compute the probability of getting exactly one six?  Independent events Sep 20 Bernoulli Trial-  Problem: A and B play a series of games. A lost first game. What is the probability that A wins the series? Random variable- X : Ω → R Example : Tossing two fair coins. X is the random variable denoting number of heads. Probability Mass Function(PMF)- examples Expectation, Variation, Standard deviation - with examples Linearity of expectation Sep 21-Sep 24 Solve questions from GO pdf and  Lecture Notes Sep 27 Continuous probability distributions - Probability density function Uniform random variable - Problem:Assume that X is uniform on [0, 1]. What is P (X ∈ Q)?What is the probability that the binary expansion of X starts with 0.010? Exponential random variable- Memoryless property: P (X ≥ x + y|X ≥ y) = e^ {−λx} Problem: Assume that a lightbulb lasts on average 100 hours. Assuming exponential distribution, compute the probability that it lasts more than 200 hours and the probability that it lasts less than 50 hours. Normal random variable- standard normal distribution Problem: Assume that X is Normal with mean μ = 2 and variance σ^2 = 25. Compute the probability that X is between 1 and 4. - Expectation, Variance, PDF, Cumulative function of continuous random variables Examples

posted Sep 27, 2018 | 817 views
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