Question

The weather forecast predicts an 80% chance of rain in the next hour. If rain follows a poisson distri
bution, what is the chance of rain in the next HALF hour? Comment on the difference between the
probability of rain in the next half hour versus the next hour. Before doing a calculation, what do you
expect your answer to be:
Best guess for chance of rain in next half hour:
Calculation:

Answer 1

Let X be the number of times it rains in a given interval of time t. Let be the mean number of rains per unit of time. Then,

X ~ Poisson(t)

For next hour t = 1,  X ~ Poisson()

Chance of rain in the next hour = P(X 1) = 1 - P(X = 0) = 1 - exp(-) * / 0! = 0.8

1 - exp(-) = 0.8

exp(-) = 0.2

= -ln(0.2) = 1.61

For next HALF hour t = 1/2,  X ~ Poisson(1.61/2 = 0.805)

Chance of rain in the next Half hour = P(X 1) = 1 - P(X = 0) = 1 - exp(-) * / 0! = 1 - exp(-) = 1 - exp(-0.805)

= 1 - 0.4471 = 0.5529 = 55.29%

The chance of rain in the next Half hour will be less because the duration is less as compared to one hour.

Before doing a calculation, we expect answer to be 80%/2 = 40%

Calculation: Chance of rain in the next Half hour = 55.29%