Probability Midterm 2008

Probability Midterm 2008 - Question 3 marks 20(a marks 10...

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INSTRUCTIONS: Dictionaries and Scientifc Calculators are allowed only. Question 1 ( marks 30). Defne (i)(marks 3) a random variable. (ii) (marks 9) a fnite random variable and its distribution? Give an example. (iii) (marks 9) a discrete random variable in general? Give an example. (iv) (marks 9) a continuous random variable? Give an example. Question 2(marks 20). The proportions oF three Freshman groups A, B, and C who receive IU schol- arships are respectively 6%, 7% and 8% oF the total number oF students (i.e. oF |A B C|). The percentages of new laptop owners among them are respectively 80%, 85% and 95%. A Freshman who is awarded the IU schol- arship is selected at random and is Found to have a new laptop. What is the probability that the Freshman was chosen From group C?
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Unformatted text preview: Question 3( marks 20 ). (a) marks 10 Multiply each vector by the appropriate scalar to Form a prob-ability vector: (i) (2, 3, 0, 5 ), (ii) (3, 0, -1, 3), (iii) (1, 1, 1, 1, 1), (iv) (0, 0, 0, 0, 0) (b)(marks 10) IF t = (1/4, 0, 1/2, 1/4) is a fxed point oF a stochastic matrix P, why P is not regular ? Question 4(marks 30). A saleman’s territory consists oF three cities, A, B and C. he never sells in the same city on successive days. IF he sells in city A, then the next day he sells in city B. However, iF he sells in either B or C, then the next day he is three times likely to sell in city A as in the other city. In the long run, how oFten does he sell in each oF the cities?...
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