Final answer:
The question pertains to joint probability distribution functions for discrete random variables, where each probability is between zero and one, inclusive, and the sum is one. A probability distribution table (PDF) for a random variable lists its possible values alongside their respective probabilities, and may include an expected value column.
Step-by-step explanation:
The question is about the concept of joint probability distribution functions (pdf) for discrete random variables in the field of mathematics. A discrete random variable takes on a countable number of values, and a probability distribution function (PDF) for such a variable assigns probabilities to these values such that each probability is between zero and one (inclusive), and the total sum of all probabilities is one.
To answer the question provided, without the specific values in the table, it is not possible to determine whether the pdf is uniform, dependent on specific values, or independent. However, if the joint pdf assigns the same probability to all combinations of the values of x1 and x2, then it is considered uniform. If the probabilities vary depending on the particular pair of x1 and x2, then the joint pdf is dependent on the specific values. If the probabilities of each x1 are the same regardless of the value of x2, and vice versa, the variables are independent.
Constructing a Probability Distribution Table
To construct a probability distribution table (PDF), one would list possible values of the random variable as one column, and their corresponding probabilities as another column. If the random variable X represents, for example, the number of days the men's soccer team plays soccer per week, and takes on the values 0, 1, and 2, a column for x*P(x) might be included to show the expected value calculation for each possible x.