stat400sln4 - 6-— l7 — ml STAT400 HW4 Solution 3.1-6(a...

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Unformatted text preview: 6 -— l7 — ml STAT400 HW4 Solution 3.1-6 (a) flat) 2 T’ :1: = 2, 3,4, 5,6, 7,8,9, 10, 11, 12. Figure 3.1-6: Probability histogram for the sum of a pair of dice 4 1 4 _ . 3'2“! E(X) : (-1) (6) + (0) (6) + (1) (6) —- 0, m2) = (*1)? (g) + (0)2 (3) + (1)2 (3) : g 8 . 20 E(3X2 —2X+4) =3(§) -- 2(0) +4: 3—. 3.2-6 E(X) = $499(0.001) — $1(0.999) = -$ 0.50. 5 21 —-6 _ —1 32-12 (1) 56+("1)'§é=3€”’€’ 15 21 -—6 —1 3.3-4 (3.) P(X g 5) = 0.5269; (b) P(X 2 6) z 1 —— P(X g 5) ='o.4731; (c) P(X g 7) — P(X g 6) = 0.8883 — 0.7393 = 0.1490; (,1) ,, 2 (12)(0.45) = 5.4, 0? =1 (12)(0.45)(o.55) = 2.97, or = «257 = 1.723. 3.3—6 (a) Xis 1(7, 0.15); (i) P(X 22) 0)) (ii) P(X = 1) (iii) P(X g 3) 3.3-8 (a) X 136(15, 0.2), (b) u = 15(0.2) = 3, a2 2 15(0.2)(0.8) : 2.4, a 2: v2.4 2 1.549; (c) P(X 2 5): 1 — P(X g 4) = 1 — 0.8358 2 0.1642. 3.3-10 (a) X is b(6, 0.05); (b) p = 6(0.05) 2 0.3; (i) P(X = 0) ' (C) (ii) (iii) P(X g 1) P(X 3 2) 1 ~— P(X g 1) = 1 -— 0.7166 = 0.2834; P(X g 1) - P(X g 0) 1 0.7166 —- 0.3206 2 0.3960; 0.9879. or2 = 6(0.05)(0.95) = 0.285; 0.7351; 0.9672; 1 — P(X S 1) = 0.0328. ...
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