3. A flea jumps at random on a plane, with jumps of constant length a, in a random direction at each step. We assume the

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3 A Flea Jumps At Random On A Plane With Jumps Of Constant Length A In A Random Direction At Each Step We Assume The 1 (59.78 KiB) Viewed 78 times

Only b section will be answer
3. A flea jumps at random on a plane, with jumps of constant length a, in a random direction at each step. We assume the flea starts from the origin, and model its position after n jumps as (Xn, Yn), where n п Xn = į a cos Ꮎ , - Yn = a sin Oj, = i=1 i=1 and O1, O2, ... are independent uniform random variables on [0, 27). , a) Show that E(X,Y1) = E(X)E(Y) = 0 for each n. b) By considering the events independent. {x1 > m } and {vi > *}, show that Xị and Yi are not ?