I have a question in my homework:
Time interval: $1$ Hour
Divide that time to $4$ Equal periods, without overlap, each period $15$ Mins long.
If in that interval, there are $20$ Occurrences of the event, what is the probability that in each $15$ Mins occurs exactly $5$ Events.
My try: It seems to me like poisson distribution, with $\lambda = 20$ And $t = 0.25$ Therefore: $\lambda t = 5$.
Therefore i should get:
$$ P(i = 5) = exp(-\lambda t) \frac{(\lambda t)^i}{i!} = exp(-5) \frac{5^5}{5!} = 0.175 $$
Yet, i have options to the answer, none of them is my answer.
What did i do wrong?
Thanks.
Straight combinatorics:
Probability
$$= \frac{N\text{(umerator)}}{D\text{(enominator)}} $$
with
$$D = 4^{(20)}.$$
How many ways are there of selecting 5 events for each time period.
$$N = \binom{20}{5}\binom{15}{5}\binom{10}{5}.$$
Final answer:
$$\frac{N}{D}.$$