Question

Refer to the Chance (Summer, 2007) article on phishing attacks at a company, Exercise 2.24 (p. 38). Recall that phishing describes an attempt to extract personal/financial information through fraudulent email. The company set up a publicized email account-called a "fraud box"-which enabled employees to notify them if they suspected an email phishing attack. If there is minimal or no collaboration or collusion from within the company, the interarrival times (i.e., the time between successive email notifications, in seconds) have an approximate exponential distribution with a mean of 95 seconds.

b. Data for a sample of 267 interarrival times are saved in the PHISHING file. Do the data appear to follow an exponential distribution with beta = 95? (Compare the sample mean and standard deviation with the mean and standard deviation if data follow an exponential distribution and then draw a conclusion)

Answer 1

To determine if the data follow an exponential distribution with beta = 95, compare the sample mean and standard deviation with the theoretical mean and standard deviation. If they are close, the data may follow an exponential distribution.

Step-by-step explanation:

To determine if the data follow an exponential distribution, we can compare the sample mean and standard deviation with the theoretical mean and standard deviation for an exponential distribution with beta = 95.

The mean for an exponential distribution is equal to the rate parameter, which in this case is 1/beta. So the theoretical mean for this distribution is 1/95 = 0.0105.

The standard deviation for an exponential distribution is equal to the rate parameter as well. So the theoretical standard deviation for this distribution is also 1/95 = 0.0105.

We can calculate the sample mean and standard deviation using the data provided in the PHISHING file. If the sample mean and standard deviation are close to the theoretical mean and standard deviation, then we can conclude that the data follow an exponential distribution with beta = 95.