Hi Gianluca!

For the first question, I want them to be threated like constant. But instead of getting the expected output:

0.2 + dt uz[1]

I am getting the output

1. (0.2 + 1. dt uz[1.])

I wonder what am I doing wrong.

For what concerns the second question... Is there a way to get to compute Moment[x,1] where x has been defined earlier following a given distribution?

Thank you very much for your kind reply!

As a workaround, you may try avoiding floating point numbers if you can:

dist = NormalDistribution[0, Sqrt[3/10]]; 
expression = 1/5 + dt (uz[1] + wz[1]); 
expectation = Expectation[expression, wz[1] \[Distributed] dist]

It takes time to get used to how the language works.

The symbols dt and uz are treated by Expectation as constants, not as random variables, unless you declare an explicit distribution for them. This is similar to what happens for example with Integrate[a x, x], where the parameter a is treated as constant.

The expression wzArray[[1]] is simply wz[1], and you cannot feed it to Moment. Your declaration

wzArray[[1]] \[Distributed] NormalDistribution[0, Sqrt[0.3]]

is not used by Moment. This works:

Moment[NormalDistribution[0, Sqrt[0.3]], 1]

This behaviour is similar to the following:

In[29]:= x == 0
Integrate[1/x, x]

Out[29]= x == 0

Out[30]= Log[x]

where the equation x == 0 is ignored by Integrate.