The average time between trades for a high-frequency trading investment firm is 40 seconds. Assume the time between trades is exponentially distributed. 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

Since the time between trades is exponentially distributed with a rate parameter of λ = 1/40 (since average time = 1/λ), the probability density function for time between trades is given by f(t) = λe^(-λt).

To find the probability that the time between trades for a randomly selected trade and the one proceeding it is less than 20 seconds, we can use the cumulative distribution function (CDF) of the exponential distribution, which is given by F(t) = 1 - e^(-λt).

So, P(time between trades < 20 seconds) = P(t < 20) = F(20) 
= 1 - e^(-λ*20) 
= 1 - e^(-(1/40)*20) 
= 1 - e^(-0.5) 
≈ 0.3935.

Therefore, the best choice is B.

The Average Time Between Trades for a High-Frequency Trading Investment