Question

is the random variable given in the accompanying table discrete or continuous? explain.
the random variable given in the accompanying table is

number of girls, x 0 1 2 3 4
p(x) 0.063 0.250 0.375 0.250 0.063

Explanation:

A discrete random variable has a countable number of possible values. In this case, the number of girls \(x\) can take on the values \(0,1,2,3,4\), which are distinct and countable. A continuous random variable would take on an uncountable infinite number of possible values (e.g., measurements like height, weight over an interval). Since the number of girls is a countable - valued variable (you can't have a fraction of a girl in this context), it is discrete.

Answer:

The random variable is discrete. It is discrete because the number of girls \(x\) (values \(0,1,2,3,4\)) is a countable set of values.