1138 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 



Since there are 3 ! = 6 ways of ordering 3 epochs, the third moment may 

 be written 



E[M\T)] = I-, f dt f du f dv <p{t - u,u - v) 

 I^ Jo Jo Jo 



= b' + ~ [ dt f du f dv[g{t -w)+ g{u -v) -^ g{t - v)] 

 l'^ Jo Jo Jo 



Here the first triple integral is immediately evaluated by use of the identity 



2 f dt f du [ dv[g{t - u) + g{u - v) + g{t - v)] 

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= I I I dtdudv g{\ t-v\) 

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= 2r f dxg{x){T -x) 

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The last triple integral, by successive inversions of integration order, turns 

 out to be 



(27) 



(28) 



