Question

Consider a finite random variable X that takes values x1, x2, …, xn with probabilities p1, p2, …, pn such that pi>0 and Σi.

Answer 1

The random variable X represents the number of occurrences or successes in a finite set of trials. It is a discrete random variable with a probability distribution function (PDF) or probability mass function (PMF).

Step-by-step explanation:

The random variable X represents the number of occurrences or successes in a finite set of trials. It is a discrete random variable since the values are countable.

The values that X may take on are determined by the possible outcomes of the trials. For example, if the trials involve flipping a coin, X may take on values 0 (no heads), 1 (one head), 2 (two heads), and so on.

The distribution of X is given by the probabilities associated with each possible value. This distribution is often represented using a probability mass function (PMF) or a probability distribution function (PDF) that assigns probabilities to the values of X. The sum of these probabilities must be equal to 1.