13. Given the following probability distribution, find: 0.3 0.5 0.2 A) mean E()

Question

13. Given the following probability distribution, find: 0.3 0.5 0.2 A) mean E() B) standard deviation 14. In one town, te number of burglaries in a week has a Poisson distribution with parameter -3.1. Find the probability that a randomly selected week the number of burglaries is at least one. 15. In Greensboro, the number of homicides in a month has a Poisson distribution with parameter à 2.0 Determine the mean and the standard deviation. table is shown below. Determine both a) PAjD) and b) P(D A) 17 16 14 30 Page 4

Explanation / Answer

#13.
A) E(X) = 3*0.3 + 4*0.5 + 7*0.2 = 4.3

B)

variance = (20.5 - 3*4.3)/2 = 3.8

sd = sqrt(3.8) = 1.9494

#14.
lambda = 3.1

P(X >= 1) = 1 - P(X = 0)

P(X = 0) = e^-3.1*(3.1)^0/0! = 0.0450

P(X >= 1) = 1 - 0.0450 = 0.955 (required probability)

#15.
mean = 2
std. dev. = sqrt(2) = 1.4142

#16.
P(A|D) = P(A and D)/P(D) = 10/17

P(D|A) = P(A and D)/P(A) = 10/116 = 5/8

x f(x) x^2*f(x) 3 0.3 2.7 4 0.5 8 7 0.2 9.8 20.5

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