Question

Determine whether the random variable is discrete or continuous. In each case, state the possible values of the random variable.

a. The number of free-throw attempts before the first shot is made.

b. The time it takes for a light bulb to burn out.

(a) Is the number of free-throw attempts before the first shot is made discrete or continuous?

A. The random variable is discrete. The possible values are

B. The random variable is continuous. The possible values are

C. The random variable is continuous. The possible values are x = 0, 1, 2, ....

D. The random variable is discrete. The possible values are x = 0, 1, 2, ...,

Answer 1

The number of free-throw attempts before the first shot is made is a discrete random variable with possible values x = 0, 1, 2, ... The time it takes for a light bulb to burn out is a continuous random variable with possible values as any positive real number.

Step-by-step explanation:

The number of free-throw attempts before the first shot is made is a discrete random variable. This is because the values of the random variable are obtained by counting the number of attempts, which means the values are countable. The possible values are x = 0, 1, 2, .... Each value corresponds to the number of attempts made before a successful shot is made.

The time it takes for a light bulb to burn out is a continuous random variable. This is because the values of the random variable are obtained by measuring the time, which means the values are not countable. The possible values can be any positive real number, such as 1.5 hours, 2.3 hours, or 4.7 hours.