Understanding Probability Distribution and Expected Value

The video tutorial explains how to calculate the expected value or mean of a discrete random variable, using household size as an example. It covers the probability distribution of household sizes, organizing data in a table, calculating the product of outcomes and probabilities, and summing these products to find the expected value. The expected household size is calculated to be approximately 3.07.

What is the range of household sizes considered in the probability distribution?

• 2 to 5

• 2 to 6

• 1 to 5

• 1 to 6

What is the main objective when analyzing the probability distribution of household sizes?

• To find the median

• To find the variance

• To find the mode

• To find the expected value

What is the first step in calculating the expected value of a discrete random variable?

• Sum the probabilities

• Find the median

• Organize data in a table

• Calculate the variance

For a household size of 2, what is the product of the outcome and its probability?

• 0.15

• 0.17

• 0.32

• 0.34

What is the probability of a household size of 3?

• 0.17

• 0.20

• 0.32

• 0.15

What is the probability of a household size of 4?

• 0.20

• 0.14

• 0.02

• 0.32

What is the product of the outcome and probability for a household size of 5?

• 0.12

• 0.14

• 0.7

• 0.8

What is the probability of a household size of 6?

• 0.32

• 0.14

• 0.20

• 0.02

What is the final expected value of the household size?

• 4.07

• 3.07

• 5.07

• 2.07

What does the expected value of 3.07 indicate about the household size?

• The most common size is 3

• The smallest size is 3

• The average size is approximately 3.07

• The largest size is 3