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### Probability and Statistics Topic Indexes

- Basic Statistics.
- Bayesian Statistics and Probability
- Calculus-Based Statistics
- Descriptive Statistics: Charts, Graphs and Plots.
- Probability.
- Binomial Theorem.
- Definitions for Common Statistics Terms.
- Critical Values.
- Hypothesis Testing.
- Normal Distributions.
- T-Distributions.
- Central Limit Theorem.
- Confidence Intervals.
- Chebyshev’s Theorem.
- Sampling and Finding Sample Sizes.
- Chi Square.
- Online Tables (z-table, chi-square, t-dist etc.).
- Regression Analysis / Linear Regression.
- Non Normal Distributions.

### Technology Topic Indexes

- Online calculators.
- Microsoft Excel for Statistics.
- TI 83 for elementary statistics.
- Using the TI 89 for statistics.
- SPSS Statistics.
- Statistics Help.
- What is the best calculator for statistics?

## Misc.

## What is Probability and Statistics?

“Probability and Statistics” usually refers to an *introductory course* in probability and statistics. The “probability” part of the class includes calculating probabilities for events happening.

While it’s usual for the class to include basic scenarios like playing cards and dice rolling at first, these basic tools are used later in the class to find more complex probabilities, like the probability of contracting a certain disease using Bayes’ theorem.

The “statistics” part of probability and statistics includes a wide variety of methods to find actual statistics, which are numbers you can use to generalize about a population. For example, you could calculate the height of all your male classmates and find the mean height to be 5’9″; That is a statistic. But then you could take that statistic and say “I think the average height of an American male is 5’9″. How accurate your guess is depends on many factors, including how many men you measured and how many men are in the entire population. Statistics are useful because we often don’t have the resources to measure, survey or poll every member of a population, so instead we take a sample (a small amount).

We also cover the basics for calculus-based statistics. As an example, you’ll need to know definite integrals to evaluate probabilities for some random variables (X):

The probability that a ≤ X ≤ b is:

Where f_{X} is the pdf of X.