Let be (A(t)) the forward and (B(t)) the backward recurrence times of an ordinary renewal process at

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Let be \(A(t)\) the forward and \(B(t)\) the backward recurrence times of an ordinary renewal process at time \(t\). For \(x>y / 2\), determine functional relationships between \(F(t)\) and the conditional probabilities

(1) \(P(A(t)>y-t \mid B(t)=t-x), 0 \leq x

(2) \(P(A(t) \leq y \mid B(t)=x), 0 \leq x0\).

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