(10 points) Ben, Max, and Yolanda are at the front of three separate lines in the cafeteria waiting to be served. The serving times for the three lines follow independent Poisson processes with respective parameters 1, 2, and 3. (a) Find the probability that Yolanda is served first. (b) Find the probability that Ben is served before Yolanda. (c) Find the expected waiting time for the first person served.

1/2 ; 1/3 ; 1/6

Step-by-step explanation:

Given :

Ben ~ exp(1)

Max ~ exp (2)

Yolanda ~ exp(3)

Ben :

X ~ exp(1)

Max:

Y ~ exp(2)

Yolanda :

Z ~ exp(3)

Probability that Yolanda is served first :

P(Z < (X, Y)) = Z /(x + y + z) = 3 /(1 + 2 + 3) = 3/6 = 1/2

Probability that Ben is served before Yolanda :

P(X < Z) = 1/ (1 + 2) = 1/3

Expected waiting time for first person served :

First person served = 1

Total = (1 + 2 + 3) = 6

Expected waiting time; E(x) :

E(x) : 1 / 6

step-by-step explanation:

through just a quick inspection, one can see that the graph of this cubing function starts in quadrant iii and ends in quadrant i.   when x = 0, y = 3, so the y-intercept is (0, 3).

if graphs are part of the problem statement, share them.   .

the photograph is photographer and- in the process- ourselves.

step-by-step explanation: