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 more than a minute?
A)0.2231
B)0.4869
C)0.5134
D)0.7769

Question

Quizplus · Accepted Answer

To solve this problem, we need to use the exponential distribution function.

Let X be the time between trades. Then X has an exponential distribution with parameter λ = 1/40 (since the average time between trades is 40 seconds).

We want to find P(X > 60), which is the probability that the time between trades is more than a minute.

Using the exponential distribution function, we have:

P(X > 60) = e^(-λ*60) = e^(-3/2) ≈ 0.2231

Therefore, the best choice is A, with a probability of 0.2231.