Question

(a)Your mum sells Koko at the kantamanto market. Based on past sales, she is convinced that demand each day could be 200, 250, 300 or 400 of cups of koko. The probability that demand will be 200, 250 or 300 is 0.1, 0.3 and 0.4.
What is the number of cups of koko to send to the market tomorrow if your mum is
i. risk neutral and plans using expected value approach.
ii. a risk lover
iii. if your mum planned based on your answer to (a) above , what is the average level of risk (i.e standard deviation) in terms of number of cups of koko not served or not demanded?

Answer 1

i) E(X) = 200*0.1 + 250*0.3 + 300 *0.4 + 400*0.2

= 20 + 75 + 120 + 80

= 295 cups

ii) If she is a risk lover, then she would take the one that could have generated the maximum profits, i.e 400 cups here.

iii) Variance = E(X2) - (E(X))2

E(X2) = 0.1 * 40000 + 0.3 * 62500 + 0.4 *90000 + 0.2 *160000

= 4000 + 18750 + 36000 + 32000

= 90750 cups

Variance = 90750 - 87025

= 3725 cups

Standard devaition = Square root of variance

= 61 cups Answer

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