Symbolic Expectation Value Evaluation

Asked Oct 23 '16 at 06:12

Active Oct 23 '16 at 16:09

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Suppose an expression $Y=a +b X$, where $X$ is a random variable. I would like to find the 2nd order central moment of $Y$ in terms of the expectation value of $X$. For example,

$$E[Y] = a + b E[X]$$

and

$$E[Y^2] = a^2 + 2a b E[X] + b^2E[X^2]$$

which gives

$$Var(Y) = E[Y^2] - E[Y]^2 = b^2E[X^2] - b^2E[X]^2$$

Can this be done using Mathematica? I am new to this environment, so please pardon me if I have not shown enough effort.

Arvind

edited Oct 23 '16 at 16:09

wolfies

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asked Oct 23 '16 at 06:12

arvindrajan92

Have a look at Expectation. – b.gates.you.know.what Oct 23 '16 at 07:42
@b.gatessucks but this requires the distribution to be known, which is not the case in this problem – arvindrajan92 Oct 23 '16 at 08:26
The distribution does not need to be known for the OP's purpose. As an aside (without answering the more general question the OP has asked), if $Y= a + b X$, then directly $Var(Y) = b^2 Var(X)$ (which is what you obtained the hard way). – wolfies Oct 24 '16 at 15:31

Symbolic Expectation Value Evaluation

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