In 1898 L. J. Bortkiewicz published a book entitled The Law of Small Numbers. He used data collected over 20 years to show that the number of soldiers killed by horse kicks each year in each corps in the Prussian cavalry followed a Poisson distribution with a mean of 0.62.(a) What is the probability of more than one death in a corps in a year?

(b) What is the probability of no deaths in a corps over 7 years?

Round your answers to four decimal places (e.g. 98.7654).

Answers

Answer 1
Answer:

Answer:

(a) The probability of more than one death in a corps in a year is 0.1252.

(b) The probability of no deaths in a corps over 7 years is 0.0130.

Step-by-step explanation:

Let X = number of soldiers killed by horse kicks in 1 year.

The random variable X\sim Poisson(\lambda = 0.62).

The probability function of a Poisson distribution is:

P(X=x)=(e^(-\lambda)\lambda^(x))/(x!);\ x=0,1,2,...

(a)

Compute the probability of more than one death in a corps in a year as follows:

P (X > 1) = 1 - P (X ≤ 1)

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

             =1-(e^(-0.62)(0.62)^(0))/(0!)-(e^(-0.62)(0.62)^(1))/(1!)\n=1-0.54335-0.33144\n=0.12521\n\approx0.1252

Thus, the probability of more than one death in a corps in a year is 0.1252.

(b)

The average deaths over 7 year period is: \lambda=7*0.62=4.34

Compute the probability of no deaths in a corps over 7 years as follows:

P(X=0)=(e^(-4.34)(4.34)^(0))/(0!)=0.01304\approx0.0130

Thus, the probability of no deaths in a corps over 7 years is 0.0130.


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Answers

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