On Sunday, 8 October 2017 01:10:14 UTC-4, Francesco Bonazzi wrote:
>
> This result is definitely wrong.
>
Sorry, ignore my previous answer, that result is correct. If you sum *n + n*,
you are summing the same random value. To get the effect of summing two
uniform distributions, just define a new uniform distribution:
In [8]: m = Uniform('m', 0, 1)
In [9]: density(n+m)
Out[9]:
⎛⎧ 1 ⎞ ⎛⎧
⎜⎪ 0 for ─── < 1⎟ ⎜⎪
⎜⎪ │z│ ⎟ ⎜⎪
z ↦ - ⎜⎨ ⎟ + ⎜⎨
⎜⎪ ╭─╮0, 2 ⎛2, 1 │ 1⎞ ⎟ ⎜⎪ ╭─╮0, 2 ⎛2, 1 │
⎜⎪z⋅│╶┐ ⎜ │ ─⎟ otherwise ⎟ ⎜⎪z⋅│╶┐ ⎜ │
─
⎝⎩ ╰─╯2, 2 ⎝ 1, 0 │ z⎠ ⎠ ⎝⎩ ╰─╯2, 2 ⎝ 1, 0 │
p
1
⎞
0 for ─────── <
1⎟
│z - 1│
⎟
⎟
1 ⎞ ╭─╮0, 2 ⎛2, 1 │ 1 ⎞
⎟
────────────────⎟ - │╶┐ ⎜ │ ─────────────────⎟ otherwise
⎟
olar_lift(z - 1)⎠ ╰─╯2, 2 ⎝ 1, 0 │ polar_lift(z - 1)⎠
⎠
The integral is unable to simplify the expression, but that's another issue.
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