a. You are considering buying insurance for your new laptop computer, which you have recently bought...

a. You are considering buying insurance for your new laptop computer, which you have recently bought for $1,200. The insurance premium for three years is $70. Over the three-year period there is an 10% chance that your laptop computer will require work worth $416, a 2% chance that it will require work worth $840, and a 2% chance that it will completely break down with a scrap value of $170.

Should you buy the insurance? (Assume risk neutrality.)

b. Consider the following cumulative probability distribution.


x	0	1	2	3	4	5
P(X ≤ x)	0.17	0.28	0.49	0.68	0.84	1

a. Calculate P(X ≤ 2). (Round your answer to 2 decimal places.)

b. Calculate P(X = 4). (Round your answer to 2 decimal places.)

Expert Solution

(a) Whether to buy the insurance or not will depend on the expected expense on the laptop computer over the three-year period which is equal to

{ 0.1 * 416 + 0.02 * 840 + 0.02 * (1200 - 170) } = $ 79

Since the insurance premium of $70 is less than the expected expense, you should buy the insurance.

(b) P(X <= 2) = 0.49

P(X = 4) = P(X <= 4) - P(X <= 3)

= 0.84 - 0.68 = 0.16

orchestra answered 2 years ago

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