Question

is the random variable given in the accompanying table discrete or continuous? explain.
number of girls, x 0 1 2 3 4
p(x) 0.063 0.250 0.375 0.250 0.063
the random variable given in the accompanying table is discrete because
there are a finite number of values.
at least one probability is less than 0 or greater than 1.
the probabilities are all between 0 and 1, inclusive.
the probabilities do not add up to 1.
the x - values are numbers.
the probabilities are decimal values.
the probabilities add up to 1.
there are infinitely many values, and they are countable.
there are infinitely many values, and they are not countable.

Explanation:

Step1: Recall the definition of discrete and continuous random variables

A discrete random variable has a countable number of possible values. A continuous random variable has infinitely many values that are not countable (it can take any value in an interval).

Step2: Analyze the given random variable

The random variable \(x\) (number of girls) can take values \(0,1,2,3,4\). These are distinct, separate values and the number of possible values is finite (\(n = 5\)).

Answer:

The random variable is discrete.