# Integration of probability density function

I would like to integrate the function so that I know the probability between values between 0 and 90000

MixtureDistribution[{0.43999526215889906,
0.5600047378411006}, {NormalDistribution[58745.18201580311,
15134.735419294597],
NormalDistribution[78262.1217564796, 2797.225012305396]}];


So given distribution:

dis=MixtureDistribution[
{0.43999526215889906,0.5600047378411006},
{NormalDistribution[58745.18201580311,15134.735419294597],
NormalDistribution[78262.1217564796,2797.225012305396]}];


with the PDF:

Plot[PDF[dis, x], {x, 0, 10^5}, PlotRange -> All,PlotTheme -> "Detailed"]


You can compute probability via built in function:

In[]:= Probability[0<=x<=90000,x\[Distributed]dis]
Out[]= 0.991409


which is the same as:

In[]:= NIntegrate[PDF[dis,x],{x,0,90000}]
Out[]= 0.991409

• Thank you for answer. – p_federbusch Jan 12 at 15:49

This is a quite standard way.

a[t_?NumericQ] :=  CDF[MixtureDistribution[{0.43999526215889906,
0.5600047378411006}, {NormalDistribution[58745.18201580311,
15134.735419294597], NormalDistribution[78262.1217564796, 2797.225012305396]}], t]
a[90000] - a[0]


0.991409

• Thank you for answer. – p_federbusch Jan 12 at 15:49