Learning xls-Poisson / Exponential Distributions (2.c.2)

[PDEM200]

Hi David,
I was reviewing the xls related to the Poisson vs Exponential Distribution and was hoping that you could provide some additional details about the interpretation using the second column data (Lambda =4).

On the Poisson: My understanding is that given a lambda of 4, the probability of 2 events occuring in a day is 14.7%.

It is on the Exponential that I would appreciate some clarification:

1) Is it correct to say that there is a 13.5 % probability that the next 2 events ( x value from Poisson) will take more thanthan 12 hrs to occur (eg. Y> t)?

Similarly,

2) There is an 86.5% probability that the next 2 events will occur within the next 12 hrs?

Thank you

 

[David Harper CFA FRM]

Hi Paul

(sorry for delay responding...)
You are correct about the Poisson.
However, the Exponential here refers to the Probability that the *next* single event (just one) will occur before/after a period time. In the second column, the first input assumption is 4: lambda = average of 4 events per day
Then under exponential, the input (H) = 12 so we are asking:
"What is the probability a single event will occur within 12 hours"
and given that the average number of events during the H-period = 2
(i.e., 4 per day = average of 2 per 12-hour period)
this imples a probability of 13.5% [i.e., EXP(-2)] that next even occurs *after* 12 hours and therefore 1-13.5% = 86.5% that the next (single) event occurs within/before the next 12 hours.

So, the P[Y<t], CDF = 86.5% means the Probability [time to next event <= 12 hours]

Thanks, David