risk and statistics 1

Consider the following two scenarios [Option A and Option B]: TabataInc. has the total inventory of $7,500. Currently, Tabatahas thisentire inventory stored in one warehouse. There is a 6% chance that a fire could occur. If this fire occurs, then Tabatawill lose their entire inventory.

[Option A] As an alternative to keeping their entire inventory in one warehouse, Tabatais considering separatingtheir inventory evenly into two different warehouses. Once again, there is a 6% chance that a fire could occur in each warehouse. If this fire occurs, then Tabatawould once again lose their entire inventory in that particular warehouse.

[Option B] Read about this concept in Chapter 5 of your text under the heading ‘Separation’ on pages 5.9 –5.12 in order to answer this question properly.

a.First, consider Option A. What is the probability of having zero dollars in losses? What is the probability of having $7,500 in losses? Derive the probability distribution for total dollar losses under Option A. Note that this question asks for total dollar losses, not number of losses. Hint: Think about the definition of a probability distribution and apply it in this case –we did this in Topic 4.[2 points]

b.Now consider Option B. Derive the probability distribution for total losses under Option B. Hint: In the case of Option B, you need to consider all the possible outcomes in terms of dollar amount of losses, recognizing that Tabata now has two warehouses. Further hint: consider the rules of probability as discussed in class when you derive your probability distribution. [4 points]

c.Compare the amount of riskTabatafaces under Option A vs. Option B. Which option has more risk? Justify and demonstrate your answer. Recall our discussion on standard deviation. [4 points]

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