Question

the accompanying table lists probabilities for the corresponding numbers of unlicensed software packages. what is the random variable, what are its possible values, and are its values numerical?

choose the correct answer below.

a. the random variable is ( p(x) ), which is the probability of a number of unlicensed software packages. the possible values of ( p(x) ) are 0.125 and 0.375. the values of the random value ( p(x) ) are numerical.

b. the random variable is ( p(x) ), which is the probability of a number of unlicensed software packages. the possible values of ( p(x) ) are 0.125 and 0.375. the values of the random value ( p(x) ) are not numerical.

c. the random variable is ( x ), which is the number of unlicensed software packages. the possible values of ( x ) are 0, 1, 2, and 3. the values of the random value ( x ) are not numerical.

d. the random variable is ( x ), which is the number of unlicensed software packages. the possible values of ( x ) are 0, 1, 2, and 3. the values of the random value ( x ) are numerical.

Explanation:

Step1: Recall the definition of a random variable

A random variable is a variable whose possible values are numerical outcomes of a random phenomenon. Here, \(x\) represents the number of unlicensed software packages. The values of \(x\) (0, 1, 2, 3) are numerical. \(P(x)\) is the probability of the corresponding value of \(x\). Probability \(P(x)\) is a non - negative real number (not a random variable in the sense of counting the number of items here) and its values (0.125, 0.375, 0.375, 0.125) are just probabilities assigned to the values of \(x\).

Step2: Analyze each option

• Option A: \(P(x)\) is not the random variable. It is the probability of the random variable \(x\).
• Option B: \(P(x)\) values are probabilities (numerical but not the random variable).
• Option C: The values of \(x\) (0,1,2,3) are numerical.
• Option D: Correctly states that the random variable is \(x\) (number of unlicensed software packages) with numerical values 0, 1, 2, 3.

Answer:

D. The random variable is \(x\), which is the number of unlicensed software packages. The possible values of \(x\) are 0, 1, 2, and 3. The values of the random value \(x\) are numerical.