Question

(R simulation) please show me the R codes and the output.

Suppose the waiting times (in hours) for a customer arriving in a queue shop (timed immediately after the previous customer or after time 0 in the case o very 1st customer) is distributed as exponential Exp(6). Use R to simulate the arrival times of the customers within a 2 hour period. Suppose you ended up with k customers arriving in the 2 hour period, use R to calculate PISk s 2], where Sk is the sum of the k waiting times. f the

Answer 1

Given exponential distribution at 6

Exponential distribution

f(x;$\lambda$)=$\lambda$e^-$\lambda$tx for x>=0

given Sk<=2

Therefore x is calculated at x=0,1,2

f(x<=2)=f(0)+f(1)+(f2)

=6e^-6*2*0+6e^-6*2*1+6e^-6*2*2

=6+6e^-12+6e^-24

=6+6*6.1442123533282E-6+6*3.7751345442791E-11