Question:

(a) State the strong law of large numbers.

(b) Data have been collected on response times (in minutes) at a fire station. The data are

2:7 1:8 0:8 1:4 1:2

(i) Develop a preliminary simulation model which uses a response-time distribution based on the five observations given above.

(ii) Use graph paper to draw the empirical cumulative distribution function of the response times and generate a value for response time using the random number 0:45.

(c) Give an algorithm which uses the exponential density function

g(x) = e^-x, 0 < x < ∞,

to generate the absolute value of a standard normal variable.