Suppose that our company performs DNA analysis for a law enforcement agency. We

Question

Suppose that our company performs DNA analysis for a law enforcement agency. We currently have one machine that is essential to performing the analysis. When an analysis is performed, the machine is in use for half of the day. Thus, each machine can perform at most two DNA analyses per day. Based on past experience, the distribution of analyses needing to be performed on any given day are as follows: On days with more jobs than we can perform, the law enforcement agency gives the extra jobs to our competitor. We are considering purchasing a second machine. For each analysis that the machine performs, we profit $1000. What is the yearly expected value of this new machine? (Assume 365 days per year - no weekends or holidays.)

Explanation / Answer

in given table, 1st row represent the number of jobs we need to perform per day

and 2nd row represents f(x) that is probability of we needing to to perform the given jobs...

i.e probability of we need to perform 0 jobs is 0.08 , and so on

so, lets find how many expected jobs we need to perform per day

so,

E(X) =sum ( Xi*P(Xi) ) = 0*0.08+1*0.10+2*0.12+3*0.14+4*0.17+5*0.24+6*0.05+7*0.10= 3.64

we already have 1 machine can perfom at most 2 jobs per day

so, new machine will perform 3.64-2 = 1.64 jobs per day

so,

yearly expected value of new machine = 1000*1.64*365 = 598600

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