Random Variable The accompanying table lists probabilities for the corresponding numbers of unlicensed software packages when four software packages are randomly selected in China. What is the random variable, what are its possible values, and are its values numerical?

Verified step by step guidance

1. The random variable in this problem is the 'Number of Unlicensed Software Packages' selected in a random trial. A random variable is a numerical outcome of a random phenomenon.
2. The possible values of the random variable are the numbers listed in the first column of the table: 0, 1, 2, 3, and 4. These represent the count of unlicensed software packages in the sample.
3. The values of the random variable are numerical because they represent counts, which are quantitative data.
4. The second column of the table, P(x), represents the probability associated with each value of the random variable. These probabilities must satisfy two conditions: (1) Each probability is between 0 and 1, and (2) the sum of all probabilities equals 1.
5. To verify the validity of the probability distribution, add all the probabilities in the second column: P(0) + P(1) + P(2) + P(3) + P(4). Ensure the sum equals 1 to confirm it is a valid probability distribution.

Key Concepts

Random Variable

A random variable is a numerical outcome of a random phenomenon. In this context, it represents the number of unlicensed software packages selected from a total of four. Random variables can be discrete, taking on specific values, or continuous, taking on any value within a range.

Probability Distribution

A probability distribution describes how probabilities are assigned to each possible value of a random variable. The table provided shows the probability distribution for the number of unlicensed software packages, indicating the likelihood of each outcome occurring when four packages are selected.

Discrete Values

Discrete values are distinct and separate values that a random variable can take. In this case, the possible values for the number of unlicensed software packages are 0, 1, 2, 3, and 4, all of which are numerical and represent countable outcomes.