. The following table contains the probability distribution for the number of traffic accidents (X) daily in a small town:
No of accidents (X) 0 1 2 3 4 5
P(X) 0.15 0.2 B 0.15 0.15 0.15
Determine:
6.1. B in the table
6.2. P(0 < X < 3)
6.3. P(X 3)
6.4. P(1 X < 4)
6.5. E[X]
6.6. Var(X)
6.1. B in the table is 0.2
6.2. P(0 < X < 3) = P(X = 1) + P(X = 2) = 0.20 + 0.15 = 0.35
6.3. P(X ≥ 3) = P(X = 3) + P(X = 4) + P(X = 5) = 0.15 + 0.15 + 0.15 = 0.45
6.4. P(1 ≤ X < 4) = P(X = 1) + P(X = 2) + P(X = 3) = 0.20 + 0.15 + 0.15 = 0.50
6.5. E[X] = Σ (X * P(X)) = 0*0.15 + 1*0.20 + 2*0.15 + 3*0.15 + 4*0.15 + 5*0.15 = 2.55
6.6. Var(X) = Σ [(X - E[X])^2 * P(X)] = [(0-2.55)^2 * 0.15] + [(1-2.55)^2 * 0.20] + [(2-2.55)^2 * 0.15] + [(3-2.55)^2 * 0.15] + [(4-2.55)^2 * 0.15] + [(5-2.55)^2 * 0.15] = 2.3025