The hourly number of phone calls, X1 received by a switchboard at a specific company is Poisson with parameter lambda. lambda varies independently from hour to hour according to the following exponential distribution: f( lambda ) = theta exp( - theta lambda ), lambda > 0. Answers to the following questions may depend on theta. Find an integral expression for P(X = 4|lambda 6). You do not need to evaluate the integral. Find E(X| lambda) and its distribution. Use the preceding part to calculate E(X). Assuming that the number of phone calls to the switchboard is independent from hour to hour, how many hours would be expected to have exactly 3 phone calls during a 24-hour period? Solution this may help you http://www.bama.ua.edu/~tmai/Math504/Math504Fl07HW01.pdf.

1. The hourly number of phone calls, X1 received by a switchboard at a specific company is
Poisson with parameter lambda. lambda varies independently from hour to hour according to the
following exponential distribution: f( lambda ) = theta exp( - theta lambda ), lambda > 0.
Answers to the following questions may depend on theta. Find an integral expression for P(X =
4|lambda 6). You do not need to evaluate the integral. Find E(X| lambda) and its distribution.
Use the preceding part to calculate E(X). Assuming that the number of phone calls to the
switchboard is independent from hour to hour, how many hours would be expected to have
exactly 3 phone calls during a 24-hour period?
Solution
this may help you http://www.bama.ua.edu/~tmai/Math504/Math504Fl07HW01.pdf