hiii...can someone help me please?! thxxxx
Suppose the interarrival times have the distribution
P{Xi = 1} = p
P{Xi = 2} = q = 1-p
where 0 < p < 1.
(a). By conditioning on X1, show that m(t) = 1 + p m(t-1) + q m(t-2) for t ≥ 2.
(b). Given that m(t) = A + B t + C rt for integers t≥ 0, where A, B, C and r are constants, use the equation of (a) and the values of m(0) and m(1) to find the values of those constants.
(c). Use the result of (b) to verify the Elementary Renewal Theorem for this process.
(c). Use the result of (b) to verify the Elementary Renewal Theorem for this process.