2 The number of calls received by a customer service department in 30 minutes is denoted by \(W\). It is known that \(\mathrm { E } ( W ) = 6.5\).
- It is given that \(W\) has a Poisson distribution.
(a) Write down the standard deviation of \(W\).
(b) Find the probability that the total number of calls received in a randomly chosen period of 2 hours is less than 30 . - It is given instead that \(W\) has a uniform distribution on \([ 1 , N ]\). Calculate the value of \(\mathrm { P } ( W > 3 )\).