Graduate (S) Business Administration 502

INFORMATION AND ANALYSIS
Spring 2017
 
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Answers, Chs. 4 and 5

4.5

(a) A priori classical probability

(b) Subjective probability

(c) A priori classical probability

(d) Empirical classical probability

.

4.6

(a) Mutually exclusive, not collectively exhaustive

(b) Not mutually exclusive, not collectively exhaustive

(c) Mutually exclusive, not collectively exhaustive

(d) Mutually exclusive, collectively exhaustive

5.5

Arrivals (X) Probability (P)
0 14/200 = 0.070
1 0.155
2 0.235
3 0.205
4 0.145
5 0.105
6 0.050
7 0.025
8 0.010

(a)

μ = E(X) = ∑ Xi P(Xi)

= (0) (0.070) + (1) (0.155) + (2) (0.235) + (3) (0.205) + (4) (0.145) + (5) (0.105) + (6) (0.050) + (7) (0.025) + (8) (0.010)  = 2.90

(b)

σ2 = ∑ [Xi - E(X)]2 P(Xi)

= (0 - 2.90)2 (0.070) + (1 - 2.90)2 (0.155) + (2 - 2.90)2 (0.235) + (3 - 2.90)2 (0.205) + (4 - 2.90)2 (0.145)

+ (5 - 2.90)2 (0.105) + (6 - 2.90)2 (0.050) + (7 - 2.90)2 (0.025) + (8 - 2.90)2 (0.010) = 3.14

σ = 3.14 ^ 0.5 = 1.772

.

5.15

p = 0.08, n = 20

(a) μ = n p = (20) (0.08) = 1.60

σ2 = n p (1 - p) = (20) (0.08) (1 - 0.08) = 1.472

σ = 0.95 ^ 0.5 = 1.21

(b) P (X = 0) = 0.1887

(c) P (X = 1) = 0.3282

(d) P (X >= 2) = P (2) + P (3) + P (4) + P (5) + P (6) + P (7) + . . . = 0.2711 + 0.1414 + 0.0523 + 0.0145 + 0.0032 + 0.0006 + 0.0001 + 0.0000 + . . . = 0.4831