# Math Help - Simple poisson question

1. ## 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

2. 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?

3. 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)

4. 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).