Need a little help with probability distribution! :D

[ThatPotato]

Hi there! I'm in my first year of college, and seem to have found myself in a bit of a rut with a probability question…



The average number of shooting star sightings, for an individual, in 100 years is 15. (This was in a previous question on the related scenario.)



The probability of an individual seeing a shooting star on any given day is 0.0015.

Let X be the number of shooting star sightings in the first decade of a person's 100 year life. Using the above probability, write down an appropriate probability distribution function for X. Give your reasoning behind your choice of distribution function.





At first I thought this was a definite Poisson distribution, since n -> towards infinity, and it occurs over a certain interval.
However, I’m confused because as far as I know, the Poisson distribution doesn’t need the probability given...(ie. 0.0015)... And it doesn't change regardless of whether it is the 'first' decade of a person's life, or the last.
I've tried the binomial distribution, but that requires that there are only two outcomes, and a set number of trials...Which I don't believe applies to this situation.


If someone could point me in the right direction, I’d be most grateful!

 

[Ishuda]

Hi there! I'm in my first year of college, and seem to have found myself in a bit of a rut with a probability question…



The average number of shooting star sightings, for an individual, in 100 years is 15. (This was in a previous question on the related scenario.)



The probability of an individual seeing a shooting star on any given day is 0.0015.

Let X be the number of shooting star sightings in the first decade of a person's 100 year life. Using the above probability, write down an appropriate probability distribution function for X. Give your reasoning behind your choice of distribution function.





At first I thought this was a definite Poisson distribution, since n -> towards infinity, and it occurs over a certain interval.
However, I’m confused because as far as I know, the Poisson distribution doesn’t need the probability given...(ie. 0.0015)... And it doesn't change regardless of whether it is the 'first' decade of a person's life, or the last.
I've tried the binomial distribution, but that requires that there are only two outcomes, and a set number of trials...Which I don't believe applies to this situation.


If someone could point me in the right direction, I’d be most grateful!

Something seems a little strange to me and I think we need a better statement of the problem.

First we need to agree with the number of days in 100 years and, to be definitive, I'll assume 365.25 so that in 100 years there are 36525 days.

Next, assuming shooting star sighting is uniformly spread out through out the days of a persons life, if the average number of shooting star sightings, for an individual, in 100 years is 15 then the probability of seeing one on any particular day is
p₁ = 15/36525 ~ 0.0004107
but you now say the probability of an individual seeing a shooting star on any given day is
p₂ = 0.0015

So does that mean the shooting star sighting is not uniform and, if so, what is the distribution of shooting stars which are seen by the person. Or, is the first statement 'the average number of shooting star sightings, for an individual, in 100 years is 15' just ignored? Or ...