4. Alice and Bob play the following game. First, on the two-dimensional (x, y) plane, Alice is located at (-X2,0) and Bo

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4 Alice And Bob Play The Following Game First On The Two Dimensional X Y Plane Alice Is Located At X2 0 And Bo 1 (210.53 KiB) Viewed 23 times

4. Alice and Bob play the following game. First, on the two-dimensional (x, y) plane, Alice is located at (-X2,0) and Bob at (0, -YB). Then, they both start moving toward the origin, (0,0), with the constant velocities VA, VB, ), respectively. The winner is the one who reaches to the origin earlier. > > d a υ (a) Assuming VA 1, VB 2, if XA Exp(1) and YB Exp(2) are independent, what is P (Alice wins)? Note that the time taken to travel a distance d with a constant velocity v is t . (b) (bonus) If VA, XA are iid, VB, YB are iid, XA ~ Exp(1), YB ~ Exp(2), and all four RVs are independent, ( what is P (Alice wins)? (Hint: There is a much shorter solution than integration: write down the event ‘Alice wins' in terms of VA, XA, VB, YB, note that all RVs are independent, and then use your intuition.)