Question

the hits to a website occur at the rate of 8 per minute between 7:00 p.m. and 10:00 p.m. the random variable x is the number of hits to the website between 9:31 p.m. and 9:39 p.m. state the values of λ and t for this poisson process. λ = □

Explanation:

Step1: Calculate the time interval \(t\)

The time between 9:31 P.M. and 9:39 P.M. is \(t = 9:39 - 9:31=8\) minutes.

Step2: Determine the value of \(\lambda\)

In a Poisson process, \(\lambda\) (the average number of events in the given time - interval) is calculated using the formula \(\lambda=\text{rate}\times t\). Given the rate is 8 hits per minute. So \(\lambda = 8\times t\). Since \(t = 8\) minutes, \(\lambda=8\times8 = 64\).

Answer:

\(\lambda = 64\)