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Unformatted text preview: 6 — l7 — ml STAT400 HW4 Solution 3.16 (a) ﬂat) 2 T’ :1: = 2, 3,4, 5,6, 7,8,9, 10, 11, 12. Figure 3.16: 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—. 3.26 E(X) = $499(0.001) — $1(0.999) = $ 0.50. 5 21 —6 _ —1
3212 (1) 56+("1)'§é=3€”’€’
15 21 —6 —1 3.34 (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) 3.38 (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. 3.310 (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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 Fall '05
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