Mathematical Appendixes
Appendix A. Expectation Proofs
This appendix furnishes proofs that may be studied to develop an understanding of the expected-value operator, and to explain certain statistical relationships that will aid in understanding the subject matter of this book.
Given two random variables X and Y having a joint probability distribution 
for 
…, the following theorems may be derived using the expectation operator.
Theorem A1:
Proof:
Theorem A2:
Proof:
Theorem A3:
for any constants a and b
Proof:
Theorem A3 implies that the standard deviation of 
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