# TI-82: Mean, Variance of Prob. Dist

You can use the list routines to find the mean, variance, and standard deviation of a probability distribution with the TI-82 calculator.

Unfortunately, you can't (easily) use the statistics mode. The problem with the statistics mode is that the statistics mode requires frequencies, and probabilities are relative frequencies.

Place the values of the random variables into a list. I will assume List 1.
Place the probabilities of the corresponding values into another list. I will assume List 2.

### Make sure it's a probability distribution

If you try to find the mean and variance for a probability distribution with something that isn't a probability distribution, your answers will be incorrect.

At least make sure the probabilities add up to be 1

```   sum L2
```

### Finding the mean

The mean is the sum of the product of the values and their probabilities. Since the values are in list 1 and the probabilities in list 2, this means that you need to sum the product of list 1 and list 2. Note that the parentheses are important here, otherwise the calculator will sum list 1 and multiply that sum by list 2.

```   sum (L1 * L2)
```

Alternatively, you may wish to save the mean to a variable, so that you can use it when finding the variance.

```   sum (L1 * L2) -> M
```

### Finding the variance

The variance is the sum of the product of the square of each value and its probability minus the mean squared. Use the x2 key instead of the ^ key followed by 2 in the following commands, it's a little bit faster.

```   sum (L1^2 * L2) - ( sum (L1 * L2))^2
```

If you had saved the mean before, then you could have used that

```   sum (L1^2 * L2) - M^2 -> V
```

I saved the value of the variance to the variable V so I could use it when finding the standard deviation.

### Finding the standard deviation

The standard deviation is the square root of the variance.

```   sqrt ANS
```

The Square root key is on the left, 2nd x2. The ANSwer key is the second (-) key located immediately to the left of the enter key. Alternatively, if you had saved the variance to V, then you could use the command.

```   sqrt V
```

### Using the PDIST program

There is a program which the instructor has written which will find all of this information for you. It is called pdist, and you can read how to use it, although it is self-explanatory.