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02_07ans - STAT 400 Examples for(Answers Outcomes TT HT TH...

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STAT 400 Examples for 02/07/2011 ( Answers ) Spring 2011 1. A balanced (fair) coin is tossed twice. Outcomes x f ( x ) Let X denote the number of H's. Construct the probability distribution of X. S = { HH , HT , TH , TT } X = 2 1 1 0 TT 0 1 / 4 HT TH 1 1 / 2 HH 2 1 / 4 1.00 Just for fun: Outcomes x f ( x ) Suppose P(H) = 0.60, TT 0 0.40 × 0.40 = 0.16 P(T) = 0.40. HT TH 1 0.60 × 0.40 + 0.40 × 0.60 = 0.48 HH 2 0.60 × 0.60 = 0.36 1.00 1 ½ . Suppose Homer Simpson has five coins: 2 nickels, 2 dimes and 1 quarter. Let X denote the amount Bart gets if he steals two coins at random. a) Construct the probability distribution of X . Outcomes x f (x) N N 0.10 2 / 5 1 / 4 = 2 / 20 = 0.1 N D D N 0.15 2 / 5 2 / 4 + 2 / 5 2 / 4 = 8 / 20 = 0.4 D D 0.20 2 / 5 1 / 4 = 2 / 20 = 0.1 N Q Q N 0.30 2 / 5 1 / 4 + 1 / 5 2 / 4 = 4 / 20 = 0.2 D Q Q D 0.35 2 / 5 1 / 4 + 1 / 5 2 / 4 = 4 / 20 = 0.2 1.0 OR
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N 1 N 2 D 1 D 2 Q x f (x) N 1 * 0.10 0.15 0.15 0.30 0.10 2 / 20 = 0.1 N 2 0.10 * 0.15 0.15 0.30 0.15 8 / 20 = 0.4 D 1 0.15 0.15 * 0.20 0.35 0.20 2 / 20 = 0.1 D 2 0.15 0.15 0.20 * 0.35 0.30 4 / 20 = 0.2 Q 0.30 0.30 0.35 0.35 * 0.35 4 / 20 = 0.2 * do not steal the same coin twice. 1.0 OR Outcomes x f (x) N N 0.10 2 5 0 1 0 2 2 2 C C C C = 0.1 N D 0.15 2 5 0 1 1 2 1 2 C C C C = 0.4 D D 0.20 2 5 0 1 2 2 0 2 C C C C = 0.1 N Q 0.30
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