RMIN 317 Lecture Notes - Lecture 4: Second Cup, N100, Standard Deviation

• School: University of Calgary
• Department: Risk Management and Insurance
• Course: RMIN 317
• Professor: Anne Elizabeth Kleffner

Document Summary

Suppose that emily and samantha each have the same possibility of an auto accident: Each person has a 0. 20 probability of ,500 loss (also assume accident losses are uncorrelated) = li * pi = e(li) (0. 8*0) + (0. 2*2500) = per person. (li) = sqrt [. 8(0-500)2 + . 2(2500-500)2] = 1000. E(l/n) or expected average loss = 0*0. 64 + 1250*0. 16 + 1250*0. 16 + If pooling, and everyone in the pool is the same, the expected average loss of the pool is the same as each person"s expected loss. Lower probability of higher losses = lower standard deviation. (l/n) = sqrt [0. 64(-500) 2 + . 32(750)2 + . 04(2000)2] Note: this also equals the standard deviation of one individual ( (li)) divided by the square root of 2. E(l/n) = ; (same b/c the person added is the same) As n gets bigger, the ability to predict the average loss gets better.