You ar e 'vait ing on t he platform of t he first stop of
Chapter 6, Problem 6.50(choose chapter or problem)
You ar e 'vait ing on t he platform of t he first stop of a Manhattan subway line. You could ride either a local or express train to your destination, 'vhich is t he last stop on t he line . The waiting t ime X for t he next express tr ain is t he exponential random variable with E [X] = 10 minutes. The 'vaiting time Y for t he next local train is t he exponential random variable wit h E [Y] = 5 minutes. Although t he arrival times X and Y of t he tr ains are r andom and independent, t he trains' travel times are deterministic; t he local train travels from first stop to last stop in exactly 15 mi.nutes 'vhile t he express tr avels from first to last stop in exactly 5 minutes. (a) W hat is t he joint PDF fx,Y(x,y)? (b) Find P [L] t hat t he local train arrives first at t he platform? ( c) Suppose you board t he first train t hat arrives. Find t he PDF of your 'vait ing time W = min(X, Y).( d ) The t ime unt il t he first tr a in (expressor local) rea ches fina l stop is T =min(X + 5, Y + 15). F ind fr(t).( e) Suppose t he local train does arrive firstat your platform. Should you boardt he local train? J ustif'.y your ans,ver.(There may be more t han one correctans,ver.)
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