Find the probability that 4 telephone calls are received in a randomly chosen one-minute period.
A sample of 10 independent observations of \(X\) is obtained.
Find the expected number of these 10 observations that are in the interval \(2 < X < 8\).
It is also known that
\(P ( X + Y = 4 ) = \frac { 27 } { 8 } P ( X = 2 ) \times P ( Y = 2 )\).
Determine the possible values of \(\mathrm { E } ( Y )\).
Explain where in your solution to part (c) you have used the assumption that telephone calls and e-mails are received independently of one another.