Question

If the second moment of a poisson distribution is 6 , find the probability p(x ⥠2)

Answer 1

If the second moment of a possible distribution is 6 find the probability p ( x â ÿ 3 = 320 or 456 cents

Answer 2

Step-by-step explanation:

If the random variable X follows a Poisson distribution with mean

3.4, find P X = 6().

Solution

This can be written more quickly as: if X ~ Po 3.4() find

P X = 6().

Now

P X = 6()=

e

−λ

λ6

6!

=

e

−3.4

3.4()6

6!

( mean, λ= 3.4)

= 0.071604 409 = 0.072 (to 3 d.p.).

Example

The number of industrial injuries per working week in a particular

factory is known to follow a Poisson distribution with mean 0.5.

Find the probability that

(a)in a particular week there will be:

(i) less than 2 accidents,

(ii) more than 2 accidents;

(b) in a three week period there will be no accidents.

Solution

Let A be 'the number of accidents in one week', so A ~ P

0

(0.5).

(a)(i)

P A < 2()=P A ≤ 1()

= 0.9098 (from tables in Appendix 3 (p257),

to 4 d.p.)

or, from the formula,

P A < 2()=P A = 0()+ P A =1()

= e

−0.5

+

e

−0.5

× 0.5