1. ## poisson distribution qns

1. If a fair die was tossed four times in a minute, how many times would you expect even numbers to show up in a 15-minute interval?
2. The average number of accidents in a randomly chosen day at the factory is 0.7. What is the chance that there will be no accidents in any given day at the factory?

3. The number of prawns in a randomly chosen prawn dumpling is 2.2. What is the chance that there is at least one prawn in a randomly chosen dumpling?

4. Between 9a.m. and 10a.m., the reception counter of a company receives visitors at a rate of 5 per ten minutes. Assuming that the visitors arrive at random points in time, determine the probability that:
a. no visitors arrived in a randomly chose minute

b. at least one visitor arrived in a randomly chosen fifteen-minute period.

2. Originally Posted by dorwei92
1. If a fair die was tossed four times in a minute, how many times would you expect even numbers to show up in a 15-minute interval?
2. The average number of accidents in a randomly chosen day at the factory is 0.7. What is the chance that there will be no accidents in any given day at the factory?

3. The number of prawns in a randomly chosen prawn dumpling is 2.2. What is the chance that there is at least one prawn in a randomly chosen dumpling?

4. Between 9a.m. and 10a.m., the reception counter of a company receives visitors at a rate of 5 per ten minutes. Assuming that the visitors arrive at random points in time, determine the probability that:
a. no visitors arrived in a randomly chose minute

b. at least one visitor arrived in a randomly chosen fifteen-minute period.

Will you please tell us where you are having problems with these, the first is so simple if you can't do it please say so we can start at an appropriate level of explanation.

The second assume the number of accidents in a day has a Poisson distribution and just look up the definition of the Poisson point mass function and plug in zero for the number of accidents.

There is no point in discussing the third until any problems with the second are sorted, and the fourth just requires the reuse of the methods of the second and third.

CB

3. i have just started learning this new distribution so aint sure how should i apply the formula.
yup, question 1 may seem to be basic but i really have no idea how to answer.
could u enlight me?

4. Originally Posted by dorwei92
i have just started learning this new distribution so aint sure how should i apply the formula.
yup, question 1 may seem to be basic but i really have no idea how to answer.
could u enlight me?
Number of tosses in 15 minutes = (4)(15) = 60.

In a single toss, Pr(even) = 1/2.

So the mean number of even tosses is (60)(1/2) = 30.

This question has nothing to do with the Poisson distribution. It's an application of basic probability theory that you're expected to be familiar with (so it might be a good idea to go back and thoroughly review it).

5. how about the other 3 questions?
must i apply poisson distribution's formula?

6. Originally Posted by dorwei92
how about the other 3 questions?
must i apply poisson distribution's formula?
What is the probability mass function $f(k,\lambda)$ for the Poisson distribution (if that is not in your notes then stop there you have not yet covered enough material to do this question)?

$\lambda$ is the mean number of occurences in the interval of interest. To answer 2 you put $k=0$ and $\lambda=0.7$.

CB