Question

Intrusion detection systems. The Journal of Research of the National Institute of Standards and Technology (November– December 2003) published a study of a computer intrusion detection system (IDS). The IDS is designed to provide an alarm whenever unauthorized access (e.g., an intrusion) to a computer system occurs. The probability of the system giving a false alarm (i.e., providing a warning when no intrusion occurs) is defined by the symbol $\alpha$, while the probability of a missed detection (i.e., no warning given when an intrusion occurs) is defined by the symbol $\beta$. These symbols are used to represent Type I and Type II error rates, respectively, in a hypothesis-testing scenario

a. What is the null hypothesis, $H_0$?

b. What is the alternative hypothesis,$H_a$?

c. According to actual data collected by the Massachusetts Institute of Technology Lincoln Laboratory, only 1 in 1,000 computer sessions with no intrusions resulted in a false alarm. For the same system, the laboratory found that only 500 of 1,000 intrusions were actually detected. Use this information to estimate the values of $\alpha$and $\beta$.

Short answer

1. $H_0:\text{No warning given when no intrusion occurs}$
   
2. $H_a:\text{Warning given when an intrusion occurs}$
   
3. The value of $\alpha and\beta$are 0.001 and 0.5.

Step-by-step solution

Null hypothesis

a. The null hypothesis is given by:

$H_0:\text{No warning given when no intrusion occurs}$

Alternative hypothesis

b. The alternative hypothesis is given by:

$H_a:\text{Warning given when an intrusion occurs}$

Computing the value of α and β

c. The value of $\alpha$is computed as,

$$\begin{gathered} \alpha =\frac{\text{Number of computer sessions with no intrusions}}{\text{Total number of computer sessions}} \\ =\frac{1}{1000} \\ =0.001 \end{gathered}$$

The value of $\beta$is computed as,

$$\begin{gathered} \beta =\frac{\text{Number of intrusions were actually detected}}{\text{Total number of intrusions}} \\ =\frac{500}{1000} \\ =0.5 \end{gathered}$$

Therefore, the value of $\alpha and\beta$are 0.001 and 0.5.