51. A manufacturerâ€™s annual losses follow a distribution with density function

2.5

3.5

2.5(0.6) ( ) for 0.6

0 otherwise.

f x x x

⎧

⎪ > =⎨⎪⎩

To cover its losses, the manufacturer purchases an insurance policy with an annual

deductible of 2.

What is the mean of the manufacturerâ€™s annual losses not paid by the insurance policy?

I have similar steps to the solution. Instead of Y=2, for x>2, I had Y=2 for x>.74 which I obtained from solving for x when Y=2. So that when x is between .6 & .74, the loss is just C and when x is greater than .74, the loss is x. Followed this through with expected value, integral(C*Y(x),x,.6,.74) + integral(X*Y(x),x,.74,inf).

Why is this incorrect & could someone clarify the steps in the solution?

2.5

3.5

2.5(0.6) ( ) for 0.6

0 otherwise.

f x x x

⎧

⎪ > =⎨⎪⎩

To cover its losses, the manufacturer purchases an insurance policy with an annual

deductible of 2.

What is the mean of the manufacturerâ€™s annual losses not paid by the insurance policy?

I have similar steps to the solution. Instead of Y=2, for x>2, I had Y=2 for x>.74 which I obtained from solving for x when Y=2. So that when x is between .6 & .74, the loss is just C and when x is greater than .74, the loss is x. Followed this through with expected value, integral(C*Y(x),x,.6,.74) + integral(X*Y(x),x,.74,inf).

Why is this incorrect & could someone clarify the steps in the solution?

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