Question

There are 50 roofs in a neighborhood that are all 200sqft. The number of raindrops that hit a single roof in one second is a Poisson random variable with μ=2. The number of raindrops one roof is independent of the numbers of drops on other roofs. What is the expected number of roofs hit by at least 125 raindrops in one minute? What is the variance of the number of roofs hit by at least 125 raindrops in one minute?

Answer 1

The expected number of roofs hit by at least 125 raindrops in one minute is 15 and the variance is 2.

Step-by-step explanation:

To find the expected number of roofs hit by at least 125 raindrops in one minute, we need to use the Poisson distribution. The parameter μ represents the average number of raindrops per roof per second, which is 2 in this case.

The expected number of raindrops on a single roof in one minute is 60 * μ = 60 * 2 = 120. Therefore, the expected number of roofs hit by at least 125 raindrops is 120 / 200 * 50 = 15.

To find the variance of the number of roofs hit by at least 125 raindrops, we can use the formula for the variance of a Poisson distribution, which is equal to μ.

Therefore, the variance of the number of roofs hit by at least 125 raindrops is 2.