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15.3 Exercise 7

Avg difficulty 2.5

Suppose the number of entries in a contest is N∼N \sim binomial (20, 0.4). There are four questions. Let Yi be the number of questions answered correctly by the ith contestant. Suppose the Yi are iid, with common distribution

Y = [ 1 2 3 4 ] P Y = [ 0 . 2 0 . 4 0 . 3 0 . 1 ] Y = \left[1 2 3 4\right] P Y = \left[0 . 2 0 . 4 0 . 3 0 . 1\right]

Let D be the total number of correct answers. Determine E[D], Var [D]E \left[D\right] , Var \left[D\right], P(15≤D≤25)P \left(15 \leq D \leq 25\right), and P(10≤D≤30)P \left(10 \leq D \leq 30\right).

Pfeiffer, Applied Probability, 15.3 Problems on Random Selection, exercise 7

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Adapted from Applied Probability © 2009 Paul E. Pfeiffer. Licensed under CC BY 3.0. Source: Applied Probability. Imported at revision d7a0420.