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Пусть: $E(e^{2}(t))=a; \delta^{2}_{E}=b; \delta^{2}_{N}=c;$  Тогда:  $$  E(e^{2}(t+1))=(1-\frac{a+b}{a+b+c})^{2}\cdot (a+b)+(\frac{a+b}{a+b+c})^{2}\cdot c=\frac{c^{2}*(a+b)}{(a+b+c)^{2}}+\frac{c\cdot c=\frac{c^{2}\cdot (a+b)}{(a+b+c)^{2}}+\frac{c\cdot  (a+b)^{2}}{(a+b+c)^{2}}=\\=\frac{c\cdot (a+b)\cdot (c+a+b)}{(a+b+c)^{2}}=\frac{c\cdot (a+b)}{a+b+c}=\frac{\delta^{2}_{N}\cdot (E(e^{2}(t))+\delta^{2}_{E})}{E(e^{2}(t))+\delta^{2}_{E}+\delta^{2}_{N}} $$  Таким образом получаем:  $$