Question

You are the consulting actuary to a group of venture capitalists financing a search for pirate gold. It’s a risky undertaking: with probability 0.80, no treasure will be found, and thus the outcome is 0. The rewards are high: with probability 0.20 treasure will be found. The outcome, if treasure is found, is uniformly distributed on [1000, 5000]. You use the inverse transformation method to simulate the outcome, where large random numbers from the uniform distribution on [0, 1] correspond to large outcomes. Your random numbers for the first two trials are 0.75 and 0.85. Calculate the average of the outcomes of these first two trials.

Answer 1

Answers:

here, 1) F(0)=.8 and

  2) F(t) = F(0) + 0.2 * CDF of Unif[1000,5000] = .8 + 0.2 (t-1000)/4000, 1000<=t<=5000

The distribution is uniform on (1000,5000), but that's not the same as saying that the distribution is THE uniform distribution on (1000,5000). There is a probability of 0.2 of being in (1000,5000) (since 0.8 is already taken up by 0). This 0.2 is uniformly distributed in the interval. Thus you have to multiply 0.2 by 1/4000 to get the density. You should've calculated

F(t)=0.8 + 0.2(t-1000)/4000 = 0.85 here t is 2000.

so, Answers is 1000.