Question

Poisson Distribution. How do you go about finding the distribution between a range using Poisson distribution? Photo is attached.

Answer 1

for part a) i know X=3, and lambda = (2.5*2) = 5
then i used the formula and crunched for P(x=3) \[P(x=3) = \frac{ 5^{3} e ^{-5} }{ 3! } = 0.1404\]

part b) P(25<=x<=50) = ?
I was thinking about integration but I am not sure if that is the right way.

Answer 2

Or since the question asked for between, find the midpoint?

Answer 3

i tried adding 25 and 50... but i don't feel it is correct

Answer 4

i think you have to use exponential distribution

Answer 5

poisson is a discrete random variable, the probability of P(n) for integer values

Answer 6

lets see

Answer 7

$$
\Large { P(a \leq x \leq b ) = e^{-\lambda a} - e^{-\lambda b }




}
$$

Answer 8

i have lambda to be 0.9375, do you agree?

Answer 9

how did you get this lambda

Answer 10

sorry, i made a mistake, it's .4, inverse of the mean.

Answer 11

right, that sounds better

Answer 12

2.5 eruptions per 100 years = .025 eruptions per year

Answer 13

my answer is really small.= .000045

Answer 14

$$
\Large {
P(a \leq x \leq b ) = e^{-\lambda a} - e^{-\lambda b }
\\ \therefore \\
P(25 \leq x \leq 50 ) = e^{-\frac{2.5}{100}\cdot 25} - e^{-\frac{2.5}{100}\cdot 50 }
= 0.2487566
}


$$

Answer 15

that is a different approach to obtain the lambda. I didn't think of it but it looks correct since the probability can be at 25th and it is 0.25

Answer 16

is this a multiple choice question

Answer 17

It is a practice exam, showing the workings gives the points.

Answer 18

is .2487 correct?

Answer 19

I do not know. The professor will be posting the answers later.