SMITH AND POLACHECK: ANALYSIS OF SIMPLE MODEL 



Appendix I. — Expressions for the variance components of N,. 

 Expression for the right hand terms of Equation (9) are: 



^ »/ \.n (i+R,), 



2 V(X)(^ = 2 V(if) -^ ^ 



(ii) 



;?, ^<«>' br = ,?, v<«/' — -i-> — ) • ""> 



\ '/ \(i+R.)^^n.^^(i.R,)/ 



Appendix II. — Coefficient of variation of a sum of random variables. 



The following is a proof that the coefficient of variation of a sum of two independent random variables is 

 smaller than the greatest CV for either of the random variables if the expected value of the random 

 variables is greater than zero. 

 If A and 5 are independent random variables such that 



E(A) = a>Q E(B) = &>Oand 



then 



CV(A) = ^^^>«=CV(B) 



V(A) ^ V(B) 



V(A)(62 + 2ab) > YiB)a^ , 



V{A)ib^ + 2ab) + YiA)a^ > YiB)a^ + Y{A)a^ , 



V(A)(a + bf > [V(B) + V(A)]c2, 



V(A) Y{B) + V(A) ^ V(A + B) 

 a^ (a + 6)2 [E(A + B)f ' 



CV(A) > CV(A + B) . 



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