Exhibit 6-4.The average time between trades for a high-frequency trading investment firm is 40 seconds.Assume the time between trades is exponentially distributed. Refer to Exhibit 6-4.What is the probability that the time between trades for a randomly selected trade and the one proceeding it is less than 20 seconds?

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Quizplus · Accepted Answer

The exponential distribution is defined by the rate parameter λ, which is the reciprocal of the mean. Here, λ = 1/40. The probability that the time between trades is less than 20 seconds is given by P(X < 20) = 1 - e^(-λ*20) = 1 - e^(-0.5) ≈ 0.3935.