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Textbook by: Barbara Illowsky, Ph.D., Susan Dean. E-mail the authors

# Practice 1: Discrete Distribution

Summary: This module provides students an opportunity to practice applying concepts related to discrete distributions. This practice exercise asks students to calculate several values based on the data provided.

## Student Learning Outcomes

• The student will analyze the properties of a discrete distribution.

## Given:

A ballet instructor is interested in knowing what percent of each year's class will continue on to the next, so that she can plan what classes to offer. Over the years, she has established the following probability distribution.

• Let XX = the number of years a student will study ballet with the teacher.
• Let P(x)P(x) = the probability that a student will study ballet xx years.

## Organize the Data

Complete the table below using the data provided.

Table 1
x P(x) x*P(x)
1 0.10
2 0.05
3 0.10
4
5 0.30
6 0.20
7 0.10

### Exercise 1

In words, define the Random Variable XX.

### Exercise 2

P(x = 4) =P(x = 4) =

### Exercise 3

P ( x < 4 ) = P(x<4)=

### Exercise 4

On average, how many years would you expect a child to study ballet with this teacher?

## Discussion Question

### Exercise 5

What does the column "P(x)P(x)" sum to and why?

### Exercise 6

What does the column "x*P(x)x*P(x)" sum to and why?

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##### Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

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Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

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