PMF and expected value

The number N of residential homes that a fire company can serve depends on the distance R (in city blocks) that a fire engine can cover in a specified (fixed) period of time. If we assume that N proportional to the area of a circle R from the firehouse, then N=C(pi)R^2, where C is a constant, R is a random variabledenoting the number of blocks that a fire engine can move in the specified time intercal. For a particular fire company C=8 and the PMF of R is shown below. Find the expected value of N, the number of homes the fire department can serve.

TABLE
{R= r}[21] [22] [23] [24] [25] [26]
P{R= r}[.05] [.20] [.30] [.25] [.15] [.05]

Please see the attached file.

The number N of residential homes that a fire company can serve depends on the distance R (in city blocks) that a fire engine can cover in a specified (fixed) period of …

PMF and expected value for the number of homes the fire department can serve is determined.