## Question

###### Damian takes carc of a machine. At the end of the ath day; â‚¬ {1,2,3,4}, preventive maintenance performed. During the days, faliures can happen to the machine. Each faliure results in a cost of C1. Denote by Z(a) the number of faliures during days; and suppose Z(a) Poi(A(a)) , Where A(a) J A(-)dz. Assume A(a) In(a + 1). Denote by Y(a) the total cost per day (given and by C the preventive maintenance cost incurred at the end of the ath day: Derive E[Y (a)]: Assume that C1 =2 and C2 3. SolveEL

Damian takes carc of a machine. At the end of the ath day; â‚¬ {1,2,3,4}, preventive maintenance performed. During the days, faliures can happen to the machine. Each faliure results in a cost of C1. Denote by Z(a) the number of faliures during days; and suppose Z(a) Poi(A(a)) , Where A(a) J A(-)dz. Assume A(a) In(a + 1). Denote by Y(a) the total cost per day (given and by C the preventive maintenance cost incurred at the end of the ath day: Derive E[Y (a)]: Assume that C1 =2 and C2 3. Solve ELY (a)] min ae{123}

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