Question

Throw a fair die. The possible values are 1, 2, 3, 4, 5, 6, and each time the die is thrown the probability of a given score is 1/6. Draw a probability histogram.

This is an example of a discrete uniform distribution. All values are assumed with the same probability.

Answer 1

To draw a probability histogram for the discrete uniform distribution resulting from throwing a fair die, you'll want to represent each of the possible outcomes (1, 2, 3, 4, 5, 6) along the x-axis and their corresponding probabilities along the y-axis.

Given that this is a uniform distribution, the probability for each outcome (1 to 6) is \( \frac{1}{6} \).

Here’s a description of how the histogram would look:

1. **X-axis (Outcomes)**: This will range from 1 to 6, representing the outcomes of the die roll.
2. **Y-axis (Probability)**: This will range from 0 to approximately 0.17 to accommodate the value \( \frac{1}{6} \).

### Steps to Create the Histogram:

1. **Choose Values (x-values)**: Plot points at 1, 2, 3, 4, 5, and 6.
2. **Set Heights (y-values)**: Each of these x-values will have a height of \( \frac{1}{6} \), which is approximately 0.167.

### Histogram Structure:
```
Probability
0.2 | *
0.15| *
0.1 | *
0.05| *
0.0 | * * * * * *
1 2 3 4 5 6
Outcomes
```

### Explanation:
- Each bar has the same height, reflecting that each outcome (1 through 6) has an equal probability of \( \frac{1}{6} \).
- The bars can be colored or shaded for better visual distinction if desired.

You can create this histogram using graphing software or plotting tools like Python's Matplotlib, R's ggplot, or even by drawing it on paper.