Final answer:
To compute the probability that exactly fifteen requests are received during a particular 2-hour period with a rate of 10 requests per hour, we can use the Poisson distribution.
Step-by-step explanation:
To compute the probability that exactly fifteen requests are received during a particular 2-hour period, we can use the Poisson distribution. The Poisson distribution is used to model the number of events that occur in a fixed interval of time or space, given the average rate at which the events occur. In this case, the rate is α = 10 requests per hour.
The probability mass function (PMF) for a Poisson distribution is given by:
P(X = k) = e^(-λ) * (λ^k) / k!
where X is the random variable representing the number of events, λ is the average rate, and k is the number of events we want to find the probability for.
For this problem, we want to find the probability that exactly fifteen requests are received during a 2-hour period. Since the rate is 10 requests per hour, the average rate λ for a 2-hour period is 20. Therefore, the probability can be calculated as:
P(X = 15) = e^(-20) * (20^15) / 15!
Calculating this expression will give us the desired probability.