Since all the values are equally likely, the probability density weighting should be the same for all values in the interval `[0,6]`. Thus the density function should be constant. Since the integral of this constant `c` over the interval `[0,6]` must be `1`, we must set the constant `c` to be `1//6`. Strictly speaking, our description of the spinner is not continuous — there are lots of numbers between `2.3` and `2.4` — so we are really modeling the distribution of continuous position around the circumference of the spinner.
The distribution function `F` for this model is
| `F text[(] t text[)]` | `=` probability of a value less than `t` |
| `= int_0^t 1/6 ds = t/6` for `0 ≤ t ≤ 6`. |
The expected value for this model is
This is reasonable, since if all the values are weighted equally, we anticipate that the average value will be in the middle of the interval of possible values.