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?
A)0.1354
B)0.3935
C)0.6065
D)0.8446

Question

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.