Determine whether the random variable is discrete or continuous. in each case, state the possible values of the random variable. (a) the number of fish caught during a fishing tournament . (b) the time it takes for a light bulb to burn out .

a.- discrete   b.- continous

Step-by-step explanation: Discrete Variable. Variables that can only take on a finite number of values are called "discrete variables." All qualitative variables are discrete. Some quantitative variables are discrete, such as performance rated as 1,2,3,4, or 5, or temperature rounded to the nearest degree.

Continuous Variable. If a variable can take on any value between its minimum value and its maximum value, it is called a continuous variable; otherwise, it is called a discrete variable.

The number of fish caught during a fishing tournament is a discrete variable, and the time it takes for a light bulb to burn out is a continuous variable

Let's define what variables are. Variables are any representation of a phenomenon or property that changes over time. In simple terms, variables are "things" that change, meaning they don't have a constant value. Variables can be either discrete or continuous.

To understand these concepts it's better to understand first what continuous means, continuous variables are those which can take any value whatsoever over time. This last statement is the main idea but it's not self-explanatory, a test to check whether a variable is continuous or not is to take any 2 possible outcomes of that variable, and check if that variable can take any value between those 2 possible outcomes. If the test gives positive then our variable is continuous, if not then it's discrete.

Let's test the first question. During a fishing tournament, each person can fish only one fish at a time, therefor possible outcomes are 1 fish, or 2 fish, or 3, or 4, and so on. This means that we will never be able to get, for example, 1.5 fish (which is a value between 2 possible outcomes, 1 fish and 2 fish), therefor our variable is discrete.

Let's test the second question. The time it takes for a light bulb to burn out has many possible outcomes, examples are 1 second, 2.5 seconds, 10 minutes, etc. If we check between any of those possible outcomes, we will always be able to find a time, doesn't matter how precise, in which the light bulb could burn. This means that the time for a light bulb to burn is continuous.

Variable, Continuous, Discrete, Interval