Probability of max/min of independent random variables

[michelececcacci]

I tried looking for issues mentioning this, but i can't find anything. I don't think this is implemented, but i could be wrong.

from sympy.stats import Die, P
from sympy import Max
X = Die("", 3)
Y = Die("", 6)
P(max(X,Y)>1)
P(Max(X,Y)>1)

Both of the last 2 lines fail.
I think it would be cool if we could get the actual probability of this (since it's not computationally intensive).

[oscarbenjamin]

Using max(X, Y) will fail because max is not a symbolic function (and cannot be overloaded by a dunder).

The correct way is Max(X, Y) and in that case the error is:

In [6]: from sympy.stats import Die, P
   ...: from sympy import Max
   ...: X = Die("", 3)
   ...: Y = Die("", 6)

In [7]: Max(X, Y) > 1
Out[7]: Max(, ) > 1

In [8]: P(Max(X, Y) > 1)
---------------------------------------------------------------------------
ValueError: Overlapping Random Variables

Why does it think that the variables are overlapping? That's because you gave them both the same name (the empty string) which also explains the weird printing.

If you give them different names then you'll get an answer:

In [9]: from sympy.stats import Die, P
   ...: from sympy import Max
   ...: X = Die("X", 3)
   ...: Y = Die("Y", 6)

In [10]: Max(X, Y) > 1
Out[10]: Max(X, Y) > 1

In [11]: P(Max(X, Y) > 1)
Out[11]: 
17
──
18

In [12]: P(Max(X, Y) > 2)
Out[12]: 7/9

In [13]: P(Max(X, Y) > 3)
Out[13]: 1/2

In [14]: P(Max(X, Y) > 4)
Out[14]: 1/3

In [15]: P(Max(X, Y) > 5)
Out[15]: 1/6

In [16]: P(Max(X, Y) > 6)
Out[16]: 0

[michelececcacci]

oh, sorry. I didn't think of this