4.1 Probability Distribution Function (PDF) for a Discrete Random Variable
Listing every value a countable random variable can take beside its probability, checking the column sums to one, and reading probabilities off that table.
10 exercises
4.1 Exercise 2
Suppose Nancy has classes three days a week. She attends classes three days a week 80% of the time, two days 15% of the time, one day 4% of the time, and no days 1% of the time. Suppose one week is randomly selected.
a. Let X = the number of days Nancy ____________________.
b. X takes on what values?
c. Suppose one week is randomly chosen. Construct a probability distribution table (called a PDF t…
4.1 Exercise 4
Let P(x) = the probability that a new hire will stay with the company x years.
Complete the table using the data provided.
4.1 Exercise 6
Let P(x) = the probability that a new hire will stay with the company x years.
P(x ≥ 5) = _______
4.1 Exercise 8
Let P(x) = the probability that a new hire will stay with the company x years.
What does the column “P(x)” sum to?
4.1 Exercise 10
What is the probability the baker will sell more than one batch? P(x > 1) = _______
4.1 Exercise 12
On average, how many batches should the baker make?
4.1 Exercise 14
Use the following information to answer the next four exercises: Ellen has music practice three days a week. She practices for all of the three days 85% of the time, two days 8% of the time, one day 4% of the time, and no days 3% of the time. One week is selected at random.
Construct a probability distribution table for the data.
4.1 Exercise 16
Use the following information to answer the next five exercises: Javier volunteers in community events each month. He does not do more than five events in a month. He attends exactly five events 35% of the time, four events 25% of the time, three events 20% of the time, two events 10% of the time, one event 5% of the time, and no events 5% of the time.
Define the random variable X.
4.1 Exercise 18
Use the following information to answer the next five exercises: Javier volunteers in community events each month. He does not do more than five events in a month. He attends exactly five events 35% of the time, four events 25% of the time, three events 20% of the time, two events 10% of the time, one event 5% of the time, and no events 5% of the time.
Construct a PDF table.
4.1 Exercise 20
Use the following information to answer the next five exercises: Javier volunteers in community events each month. He does not do more than five events in a month. He attends exactly five events 35% of the time, four events 25% of the time, three events 20% of the time, two events 10% of the time, one event 5% of the time, and no events 5% of the time.
Find the probability that Javier volunteers f…
Adapted from Introductory Statistics 2e © 2023 Rice University. Licensed under CC BY 4.0. Source: Introductory Statistics 2e. Imported at revision 50ec917.