Question

Probability and Statistics

Answer 1

A random variable can be either discrete or continuous. It is discrete it can assume only a finite number of values, or a countable infinity of values at most.

It is continuous if it can assume values in an interval, or in general, an uncountable infinity of values.

That being said, we have:

Option A is a discrete random variable, because the number of heads in 5 throws can be 0, 1, 2, 3, 4 or 5. So, we have finitely many possible values.

Option B is a discrete random variable, because the number you roll on a die is either1, 2, 3, 4, 5 or 6. So, we have finitely many possible values.

Option C is a discrete random variable, because if there are n students in a class, the number of boys is an integer between 0 and n. So, we have finitely many possible values.

Option D is finally a continuous random variable, because the height of a 10-year-old can be any number (in a suitable range of course).