## Quick Reference

The mathematical rules that govern expectations. For random variables *X*, *Y*, *X** _{j}*, with expected values E(

*X*), E(

*Y*), and E(

*X*

*), and for any constants*

_{j}*a*,

*b*,

*a*

*, the following formulae hold, without any assumptions of independence:*

_{j}E(*X*+*Y*)=E(*X*)+E(*Y*),

E(*X*−*Y*)=E(*X*)−E(*Y*),

E(*aX*+*b*)=*a*E(*X*)+*b*,

E(*aX*+*bY*)=*a*E(*X*)+*b*E(*Y*),

. The following law also holds, provided *X* and *Y* are independent:

E(*XY*)=E(*X*)×E(*Y*).

*Subjects:*
Probability and Statistics.

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