Understanding Probability Distributions

The video tutorial explains how to determine if a table represents a probability distribution for a discrete probability distribution. It outlines two conditions: each probability must be between 0 and 1 inclusive, and the sum of all probabilities must equal 1. The video analyzes two tables to check if they meet these conditions, concluding that the first table does not represent a probability distribution due to a sum of 1.05, while the second table does, as its sum is exactly 1. The tutorial emphasizes careful checking of these conditions.

What are the two conditions that must be met for a table to represent a probability distribution?

• Each probability is between 0 and 1, and the sum is 0.

• Each probability is between 0 and 2, and the sum is 1.

• Each probability is between 0 and 2, and the sum is 0.

• Each probability is between 0 and 1, and the sum is 1.

What does it mean for a probability to be in the closed interval from zero to one?

• The probability must be exactly zero.

• The probability can be zero or one.

• The probability can be greater than one.

• The probability can be less than zero.

In the first table, why is it not considered a probability distribution?

• The probabilities are greater than 2.

• The probabilities are negative.

• The sum of probabilities is not 1.

• The probabilities are not between 0 and 1.

What is the sum of probabilities in the first table?

• 1.00

• 1.05

• 0.85

• 0.95

In the second table, what confirms it is a probability distribution?

• The sum of probabilities is 0.

• The sum of probabilities is 1.

• The probabilities are all negative.

• The probabilities are all greater than 1.

What is the sum of probabilities in the second table?

• 1.05

• 1.00

• 0.95

• 0.85

Why is it important to check both conditions for a probability distribution?

• To verify the table represents a valid probability distribution.

• To ensure probabilities are negative.

• To make sure the probabilities are less than 0.

• To confirm the probabilities are greater than 2.

What should you be careful about when checking probability distributions?

• The positions of yes or no answers.

• The positions of negative probabilities.

• The positions of probabilities less than 0.

• The positions of probabilities greater than 2.