Question

The Statewide Auto Insurance Company developed the following probability distribution for automobile collision claims paid during the past year:

PAYMENT ($)	Probability
0	0.83
500	0.06
1000	0.05
2000	0.02
5000	0.02
8000	0.01
10000	0.01

Set up intervals of random numbers that can be used to generate automobile collision claim payments.


Using the 20 random numbers below (first row first, left to right, simulate the payments for 20 policyholders.

0.7806	0.7370	0.2120	0.2540	0.2673	0.4927	0.1885	0.1530	0.6313	0.8631
0.9220	0.7198	0.8736	0.5875	0.5098	0.8350	0.8048	0.9573	0.2683	0.3605

How many claims are paid and what is the total amount paid to the policyholders?

a.		5, $4,500
b.		4, $4,500
c.		3, $4,500
d.		5, $3,500
e.		4, $3,500

Answer 1

The given table is -

and also given 20 random number shown as below table.

we want intervals such that a uniform random number between '0 and 1' will give you each of our ' seven' outcomes with the stated probabilities.

Thus, we need to divide the interval between '0 and 1' proportionally. This is easy to do just by cumulating the proportionalies i.e. Adding them sequentially to determine where each sub interval from ''o'' (the lower bounds of the first interval).

0.83 which gives 0.83 as the upper bounds of the first sub-interval this also serves as the lower bounds of the next sub-interval.