Identify the given item as probability distribution, continuous random variable, or discrete random variable.

The heights of buildings in a metropolitan area.

The height of the buildings is a numerical measure which can have any value. We can not limit itself to a few numbers as is the case with discrete values. Discrete Random Variables can only have certain values which they can obtain while Continuous Random Variables can have any value to any number of digits and decimals. Discrete Variables can be counted while continuous variables are measured.

Since height of a building can take any value and is not restricted to a few levels or values and is found by measuring, it is a continuous random variable.