# Simple poisson question

• Feb 28th 2009, 10:41 AM
djmccabie
Simple poisson question
Been a while since i dealt with poisson distribution any help is appreciated =]

X~Po (5)

Find probability that
i) exactly 6 are sold in a randomly chosen week
ii) exactly 6 are sold in each of 3 randomly chosen weeks
iii) exactly 18 are sold in a randomly chosen 3 week period

ok for i I use the formula (e^-λ8λ^X) / X!

which gives me (e^-5 8 5^6) / 6!

= 0.1462 (4 d.p.)

now for part ii is it the above answer cubed?? giving 3.1264 x10^-3

really cant remember how to do part iii
• Feb 28th 2009, 02:19 PM
mr fantastic
Quote:

Originally Posted by djmccabie
Been a while since i dealt with poisson distribution any help is appreciated =]

X~Po (5)

Find probability that
i) exactly 6 are sold in a randomly chosen week
ii) exactly 6 are sold in each of 3 randomly chosen weeks
iii) exactly 18 are sold in a randomly chosen 3 week period

ok for i I use the formula (e^-λ8λ^X) / X!

which gives me (e^-5 8 5^6) / 6!

= 0.1462 (4 d.p.)

now for part ii is it the above answer cubed?? giving 3.1264 x10^-3

really cant remember how to do part iii

Please define the distribution better. What exactly is X? And what is the mean of X?
• Feb 28th 2009, 07:08 PM
djmccabie
OK the bit from the beginning i missed out is

"The number of batteries sold per week by a garage may be assumed to have a Poisson distribution with a mean 5."

I just replace this with X~Po(5)
• Feb 28th 2009, 07:13 PM
mr fantastic
Quote:

Originally Posted by djmccabie
Been a while since i dealt with poisson distribution any help is appreciated =]

X~Po (5)

Find probability that
i) exactly 6 are sold in a randomly chosen week
ii) exactly 6 are sold in each of 3 randomly chosen weeks
iii) exactly 18 are sold in a randomly chosen 3 week period

ok for i I use the formula (e^-λ8λ^X) / X!

which gives me (e^-5 8 5^6) / 6!

= 0.1462 (4 d.p.)

now for part ii is it the above answer cubed?? giving 3.1264 x10^-3

really cant remember how to do part iii

ii. looks fine.

For free, let Y be the random variable number of batteries sold in a three week period. Then Y ~ Po(15). Calculate Pr(Y = 18).