4.1 Probability distribution function (pdf) for a discrete random

A child psychologist is interested in the number of times a newborn baby's crying wakes its mother after midnight. For a random sample of 50 mothers, the following information was obtained. Let $X$ = the number of times a newborn wakes its mother after midnight. For this example, $x$ = 0, 1, 2, 3, 4, 5.

$\text{P(x)}$ = probability that $X$ takes on a value $x$ .

$X$ takes on the values 0, 1, 2, 3, 4, 5. This is a discrete $\mathrm{PDF}$ because

1. Each $\text{P(x)}$ is between 0 and 1, inclusive.
2. The sum of the probabilities is 1, that is,

Suppose Nancy has classes 3 days a week. She attends classes 3 days a week 80% of the time, 2 days 15% of the time, 1 day 4% of the time, and no days 1% of the time. Suppose one week is randomly selected.