problemset5solution

problemset5solution - PAM 210 Lecture 1 Spring 2008 Problem...

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PAM 210 Lecture 1 Spring 2008 Problem Set #5 Posted: 3 rd March, 2008 Due Date: 10 th March, 2008 Round your final answers to four decimal places, if necessary. (Correct final answers get full credit. Showing work is not necessary) 4.41 (a) “At least one nonword error” is the event “X ≥ 1” (or “X > 0”). P(X ≥ 1) = 1 − P(X = 0) = 0.9 . (b) “X ≤ 2” is “no more than two nonword errors,” or “fewer than three nonword errors.” P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.1 + 0.2 + 0.3 = 0.6. P(X < 2) = P(X = 0) + P(X = 1) = 0.1 + 0.2 = 0.3 . 4.52 Let “S” mean that a student supports funding and “O” mean that the student opposes funding. (a) P(SSO) = (0.6)(0.6)(0.4) = 0.144. (b) See the top two lines of the table below. (c) The distribution of X is given in the bottom two lines of the table. For example, P(X = 0) = (0.6)(0.6)(0.6) = 0.216, and in the same way, P(X = 3) = 0.43 = 0.064. For P(X = 1), note that each of the three arrangements that give X = 1 have probability 0.144, so P(X = 1) = 3(0.144) = 0.432. Similarly, P(X = 2) = 3(0.6)(0.4)(0.4) = 0.288. (d) A majority means X ≥ 2; P(X ≥ 2) = 0.288 + 0.064 = 0.352.
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