Question

96 Diamonds found in an area 1120 square meters. The diamonds were scattered implying the area has a poisson distribution with mean 96/1120 = sites per squared meter, Under this assumption, if an area of 20 square metres are chosen:

A. List the possible values of X, number of diamonds in the chosen area of 20 square metres. What is the value of the parameter of the distribution of X in 20 square metres

From answer A find the probability in the 20 square metres of finding -

No diamonds

Exactly one diamond

More than one diamond

Answer 1

Number of diamonds found in 1120 square meters area = 96

Average number of diamond found in 1120 square meters area = 96 /1120.

Let X be number of diamond found in 20 square meters area.

m = Average number of diamond found in 20 square meters area = 20 * 96 / 1120 = 1.7143.

The probability distribution of random variable X is Poisson with parameter m = 1.7143.

The p.m.f. of X is

i) P ( no diamond found in 20 square meter area chosen) = P ( X= 0)

ii) P ( exactly one diamond found in 20 square meter area chosen) = P ( X=1)

iii) P ( more than one diamond found in 20 square meter area chosen) = P(X>1) = 1 - P(X<=1)

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

= 1 - 0.1801 - 0.3087

= 0.5112