Monte Carlo Method for Probabilities and Expectations 

Calculate the probability of an event.

In[1]:=

X NProbability[x > 1, x \[Distributed] NormalDistribution[]]

Out[1]=

Obtain an estimate based on simulation.

In[2]:=

X NProbability[x > 1, x \[Distributed] NormalDistribution[], Method -> "MonteCarlo"]

Out[2]=

Calculate the expectation for an expression.

In[3]:=

X NExpectation[x Sin[x] + 1, x \[Distributed] NormalDistribution[]]

Out[3]=

Obtain an estimate based on simulation.

In[4]:=

X NExpectation[x Sin[x] + 1, x \[Distributed] NormalDistribution[], Method -> "MonteCarlo"]

Out[4]=