Question

Each day, two students, Xavier and Yolanda, arrive independently at McDonalds for lunch at a random time between noon and 1 p.m. Let X be the time that Xavier arrives (in minutes after 12 p.m.) and Y be the time that Yolanda arrives (in minutes after 12 p.m.). X and Y are independent Uniform(a=0,b=60) random variables. all answers to 3 decimal places

a) FInd the joint p.d.f. of X and Y, then find it at f(15,25)

b) If both Xavier and Yolanda take 15 minutes to eat their lunch (after they arrive), what is the probability that they are able to meet up? (Hint: Sketch the region of times (x,y) that correspond to Xavier and Yolanda meeting up. You can calculate this probability by geometry)

c) What is the probability that Xavier arrives after Yolanda?

Answer 1