Question

The number of page requests that arrive at a Web server is a Poisson random variable with an average of 100 requests per minute. Find the probability that there are no requests in a 100-ms period.

a) e^−0.1
b) e^−10
c) e^10
d) Options are not provided.

Answer 1

To find the probability of no requests in a 100-ms period, use the Poisson distribution formula with the average requests per millisecond. The answer is approximately e^(-0.1), option a).

Step-by-step explanation:

To find the probability that there are no requests in a 100-ms period, we can use the Poisson distribution formula. The average number of requests per minute is given as 100. We can convert this to requests per millisecond by dividing by 60, so the average number of requests per millisecond is 100/60.

The formula for the Poisson distribution is P(X = k) = (e^(-λ) * λ^k) / k!, where X is the random variable representing the number of requests, λ is the average number of requests per period, and k is the number of requests we want to find the probability for.

In this case, we want to find the probability that there are no requests in a 100-ms period, so k = 0 and λ = 100/60.

Plugging these values into the formula, we get P(X = 0) = (e^(-100/60) * (100/60)^0) / 0! = e^(-100/60).

Therefore, the probability that there are no requests in a 100-ms period is approximately e^(-0.1), which is option a).