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the_integral_actuary
07-04-2011, 09:19 AM
The problem is from Actex study manual. Problem Set 8, number 33.

Q: Two insurers provide bids on an insurance policy to a large company. The bids must be between 2000 and 2200. The company decides to accept the lower bid if the two bids differ by 20 or more. Otherwise the company will consider the two bids further. Assume that the two bids are independent and both uniformly distributed on the interval from 2000 and 2200. Determine the probability that the company considers the two bids further.

I am getting 0.2 when I compute using the integral, but 0.19, when I compute the area of the region since it is uniform. The solution says 0.19 is the answer and it uses the area of the region. However, it also says you can use a double integral.

I am using x-20 and x+20 as my bounds for y, and 0 to 200 for my bounds for x. The pdf of the joint distribution is 1/40,000.

I would guess that I am using the wrongs bounds but I would appreciate some help. Thanks

the_integral_actuary
07-04-2011, 09:41 AM
Never mind i figured it out I am using the wrong bounds.