Chapter 7 Summary
Key Concepts Summary
- 7.1 Probability Distribution of a Discrete Random Variable
- Recognizing, understanding, and constructing discrete probability functions
- 7.2 Expected Value and Standard Deviation for a Discrete Probability Distribution
- Calculating and interpreting the expected values of probability distribution functions
- Calculating the standard deviation for a probability distribution
Glossary of Terms
Discrete Random Variable. A random variable expressed in countable terms (i.e. the number of phone calls made in a week).
Expected Value. The average value expected after long-term repetition of an experiment.
Law of Large Numbers. A rule stating that as the number of trials of a probability experiment increases, the difference between the expected value and observed value should decrease.
Probability Distribution. A listing of all the possible values of a random variable, and the likelihood that they will occur.
Random Variable. A description of the data being observed that may vary between repetitions of an experiment.
Formula & Symbol Hub
Symbols Used
- [latex]\sigma[/latex] = standard deviation
- [latex]P(x)[/latex] = probability of [latex]x[/latex]
- [latex]\mu[/latex] = mean or expected value
- [latex]\sum[/latex] = summation symbol
Formulas Used
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Formula 7.1 – Expected Value
[latex]\begin{eqnarray*}E(x)&=&\sum\left(x\times P(x)\right)\end{eqnarray*}[/latex]
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Formula 7.2 – Standard Deviation of a Probability Distribution
[latex]\begin{eqnarray*}\sigma&=&\sqrt{\sum\left((x-\mu)^2\times P(x)\right)}\end{eqnarray*}[/latex]
