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The time until the first arrival into a bank after it opens is an exponential random...

The time until the first arrival into a bank after it opens is an exponential random variable with standard deviation equal to 2 minutes. What is the probability that the time to the first arrival is equal to 1 minute? If your answer is non-integer, answer to four decimal places using conventional rounding methods.

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Answer #1

X is a continuous random variable since time is measured.

you must know m, the decay parameter.

m = 1/2 = 0.5

f(x) = 0.5e–0.5x where x is at least zero and m = 0.5.

, f(1) = 0.5e−(0.5)(1) = 0.8243

probability that the time to the first arrival is equal to 1 minute is 0.8243

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