The net revenue R for a newly developed antifungal spray for citrus fruit is expected to be $3.1 million per year for the next 5 years. This expected amount is based on estimates that R could be $2.6, $2.8, $3.0, $3.2, $3.4 million, all with the same probability, or $3.6 million with half the probability of the other values. (a) Write the probability statements for each of the estimates. (b) Determine the expected value of R.
What will be an ideal response?
(a) Let p = probability such the 5p plus 1/2p equals 1.0
5p + 0.5p = 1
p = 1/5.5
= 0.18182
In $ million units for R, the probability statements are:
P(R=2.6) = P(R=2.8) = ……= P(R=3.6) =0.18182
P(R=3.6) = 0.09091
(b) E(R) = 0.18182(2.6 + 2.8 + 3.0 + 3.2 + 3.4) + 0.09091(3.6)
= 2.72730 + 0.32728
= $3.05458 ($3.054 million)
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