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Hi quick question:

Suppose you have a function of random variables given in the following way

Z=X if condition A

Z=Y if condition B

where both X and Y are random variables, and conditions A & B are disjoint.

Then would the expectation of Z be

E[Z]=E[X]*Pr(A)+E[Y]*Pr(B)?

Thanks in advance.

Suppose you have a function of random variables given in the following way

Z=X if condition A

Z=Y if condition B

where both X and Y are random variables, and conditions A & B are disjoint.

Then would the expectation of Z be

E[Z]=E[X]*Pr(A)+E[Y]*Pr(B)?

Thanks in advance.

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