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 customers arriving at a bank between noon and 1 : 00 P.M.. ​(b) The amount of snowfall.

Answer 1

Answer:

(a) Discrete random variable.

(b) Continuous random variable.

Step-by-step explanation:

A random variable assumes distinct values or in a specific interval.

If a random variable assume specific distinct finite set of values, that can be counted, it is known as a discrete random variable.

If a random variable assume values in an interval, that cannot be counted, it is known as a continuous random variable.

(a)

Let the random variable X be defined as the number of customers arriving at a bank between noon and 1 : 00 P.M.

The number of customers arriving at a bank in an hour can be counted and are distinct and finite.

Thus, this is an example of discrete random variable.

(b)

Let the random variable Y be defined as the amount of snowfall.

The amount of snowfall is measured by the thickness of the snowfall. The random variable can assume value in an interval like, 1.5 cm to 3 cm snowfall. There are infinite values in this interval.

Thus, this is an example of continuous random variable.