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# Discrete Random Variables

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Author: Al Greene
##### Description:

• Introduce discrete random variables and demonstrate how to create a probability model
• Present how to calculate the expected value, variance and standard deviation of a discrete random variable

This packet has two videos teaching you all about discrete random variables. There is also a short powerpoint of definitions, and an example for you to do at the end.

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Tutorial

## What's in this packet

This packet has a powerpoint of definitions, two videos, and an example for you to do yourself. Some terms that may be new are:

• Discrete Random Variable
• Probability Model
• Expected Value
• Variance

Source: Greene

## Definitions

This powerpoint gives you the definitions of mean and standard deviation, as well as showing you how to find a missing probability in your table.

Source: Greene

## Discrete Random Variable - Definitions and Example

This video gives you the definition of a discrete random variable, and shows you an easy example of one.

Source: Greene

## Discrete Random Variables - Mean and Standard Deviation

This video shows you the formulas for mean, variance, and standard deviation for a discrete random variable. It also has an example for you to follow along with.

Source: Greene

## Example

Consider the following probability distribution table:

______________________________________________

X              |____3_____|___4______|_____5_____|_____6______|

P(X=x)     |____.12___|___.26_____|____.31_____|____________|

As you can see, the probability for 6 is missing. Do the following:

1. Find the probability that X=6.

2. Find the probability that X is less than 5.

3. Find the mean of X.

4. Find the standard deviation of X.

Source: Greene

## Example Solutions

______________________________________________

X              |____3_____|___4______|_____5_____|_____6______|

P(X=x)     |____.12___|___.26_____|____.31_____|____________|

1. Find the probability that X=6.  This can be done by adding up all the known probabilities and subtracting them from 1.

P(X=6) = 1 - (.12+.26+.31) = 1-.69 = .31

2. Find the probability that X is less than 5.  This includes the numbers 3 and 4. We see from the table that P(X=3) = .12 and P(X=4) = .26. Therefore, we just add them together.

P(X<5) = P(X=3) + P(X=4) = .12 + .26 = .38

3. Find the mean of X.  This is done using our formula from the powerpoint.

E(X) = 3*.12 + 4*.26 + 5*.31 + 6*.31 = 4.81

Find the standard deviation of X.  Once again, this is done using our formula on the powerpoint.

SD(X) = sqrt[(3-4.81)^2*.12 + (4-4.81)^2*.26 + (5-4.81)^2*.31 + (6-4.81)^2*.31] = sqrt(.393132+.170586+.011191+.438991) = sqrt(1.0139) = 1.0069

Source: Greene

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