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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