Let S; denote the time of the i-th event in a Poisson process having rate A....

 

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Let S; denote the time of the i-th event in a Poisson process having rate A. Also, let A(t) denote the age at t and Y(t) denote the excess at t. (a) P{S3>t| S2 =x} = ? (b) P{A(t) > s) = ? (c) P{A(t) > s, Y(t) >x} = ? (d) Show that A(t) and Y(t) are independent. Let S; denote the time of the i-th event in a Poisson process having rate A. Also, let A(t) denote the age at t and Y(t) denote the excess at t. (a) P{S3>t| S2 =x} = ? (b) P{A(t) > s) = ? (c) P{A(t) > s, Y(t) >x} = ? (d) Show that A(t) and Y(t) are independent.