Eo 
Nz = | | IY] p(¥,0, ¥) dY dY. (12.143) 
-< 0 
Then, the expected number of maxima regardless of magnitude per unit time will be 
o 0 
na= | J IY] p(Y,0,¥) d¥ dy. (12.144) 
Similarly the expected number of minima per unit time will be 
Ne = [ 
-o 
Because maxima and minima are paired in the same record of response N a= NG, 
from Eqs. 12.142 and 12.144, the probability that a maximum will be less than € is ap- 
proximated 
Il p(¥,0,¥) d¥ dY. (12.145) 
ou 8 
N 
Prob[Maximum < &] = 1- = (12.146) 
Similarly, 
sea 
Prob[Minimum < &] = at : (12.147) 
Then, the probability densities of maxima and minima are obtained by differentiat- 
ing Eqs. 12.146 and 12.147 with respect to &, as 
pé)= 
INE 
No 
0 
= | IY p(E,0,¥) d¥ (12.148) 
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