The following table contains the probability distribution for X = the number of

Question

The following table contains the probability distribution for X = the number of traffic accidents reported in a day in Corvallis, Oregon. X 0 1 2 3 4 5 P(X) 0.10 0.20 0.45 0.15 0.05 0.05

What is the probability that there will be at least two accidents in one day?

What is the median number of accidents in one day?

What is the probability that there will be three accidents in one day?

What is the mean or expected value of the number of accidents in one day?

What is the standard deviation of the number of accidents in one day?

Explanation / Answer

a) P(X > 2) = 1 - (P(X = 0) + P(X = 1)) = 1 - (0.1 + 0.2) = 0.7

b)

X              Cummulative probability

0                   0.1

1                   0.3

2                   0.75

3                   0.9

4                  0.95

5                   1

Median = 2

c) P(X = 3) = 0.15

d) E(X) = 0 * 0.1 + 1 * 0.2 + 2 * 0.45 + 3 * 0.15 + 4 * 0.05 + 5 * 0.05 = 2

e) E(X2) = 02 * 0.1 + 12 * 0.2 + 22 * 0.45 + 32 * 0.15 + 42 * 0.05 + 52 * 0.05 = 5.4

Var(X) = E(X2) - (E(X))2 = 5.4 - 22 = 1.4

Standadrd deviation = sqrt(1.4) = 1.1832 or 1 (approximately)

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.