2. Alice and Bob have pointed their telescopes at different parts of the night sky and are waiting to see falling stars. Let the RV X measure the time (in hrs) until Alice sees her first falling star, and the RV Y measure the time (in hrs again) until Bob sees his first falling star. Furthermore, assume X, Y have joint PDF: (2e-T-24, x > 0, y>0 fx,x (x, y) = otherwise (a) (7 points) Derive the joint CDF of X, Y and use it to find the probability that it takes Alice at least 1hr to see a falling star (irrespective of the time it takes Bob). (b) (6 points) Find the probability that Alice sees a falling star before Bob