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Two turtles are racing. Turtle A’s time is exponentially distributed with mean 2 minutes. Turtle B’s...

Two turtles are racing. Turtle A’s time is exponentially distributed with mean 2 minutes. Turtle B’s time is exponentially distributed with mean 3 minutes. Assume that their times are independent.

a) What is the probability that turtle A wins?
b) What is the expected time of the winner? What is its variance? c) What is the pdf of the time difference between the loser and the winner (by how much the faster turtle wins)?

Math   Statistics-And-Probability   
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