Question

A random variable is said to be discrete if?

1) Its outcomes are countable
2) It can assume any real number within a given interval
3) The rules of probability apply
4) It can be represented graphically

Answer 1

A random variable is discrete if its outcomes are countable. Discrete random variables result from processes like counting specific occurrences. Their probability distribution function must have probabilities between zero and one, inclusive, and the sum of all probabilities must equal one.

Step-by-step explanation:

A random variable is said to be discrete if its outcomes are countable. This means that the values of a discrete random variable are obtained by counting such as the number of red balls, the number of heads in a coin toss, or the number of books in a backpack. In contrast, a continuous random variable has outcomes that are uncountable, meaning they are obtained by measuring, like the temperature on a given day or the height of a high school student.

The probability distribution function (PDF) for a discrete random variable has two essential characteristics:

1. Each probability is between zero and one, inclusive.
2. The sum of the probabilities is one.

These characteristics ensure that the probabilities are properly normalized and that they represent a complete and exclusive set of all possible outcomes of the random variable.