Exam1Sample

Exam1Sample - Random Sampling of Questions 1 The probability that rain is followed by rain is 0.8 a sunny day is followed by rain is 0.6 Find the

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Random Sampling of Questions 1. The probability that rain is followed by rain is 0 . 8, a sunny day is followed by rain is 0 . 6. Find the probability that one has two rainy days then two sunny days. 2. Let: f ( x ) = k | x - 2 | , for x = - 1 , 0 , 1 , 3 Find k so that f is a PDF. Find the expected value of X . Find the expected value of X 2 . 3. A balanced die is tossed twice. Let A be the event that an even number comes up on the first toss. Let B be the event that an even number comes up on the second. Let C be the event that the first two tosses gave the same number. Are A,B,C pairwise independent independent? 4. State Bayes’ Theorem. 5. If A,B are independent prove that A 0 and B 0 are independent. 6. What is the difference between saying that A,B,C are independent events, versus saying that X,Y,Z are independent random variables? 7. In a poker game, 5 cards are dealt from a deck of 52. What is the proba- bility of getting a four-of-a-kind? 8. If the joint PDF is given by:
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This note was uploaded on 12/16/2011 for the course CS cs102 taught by Professor Rsharma during the Spring '11 term at IIT Kanpur.

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Exam1Sample - Random Sampling of Questions 1 The probability that rain is followed by rain is 0.8 a sunny day is followed by rain is 0.6 Find the

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