1 Ricks Toy Store faces the following probability distributi

1) Rick’s Toy Store faces the following probability distribution of fire losses in its store over the next year:
Probability Loss

a. Calculate the expected value and standard deviation of Rick’s losses for the year.
b. Assume that Rick pools his losses with Mark’s store, which has an identical loss distribution. Mark’s losses are independent of Rick’s. Rick and Mark agree to split the total losses in the pool equally. Show the revised probability distribution for the mean loss from the pool.
c. Calculate the expected value and standard deviation of the pooled mean losses
d. Insures combine a large number of exposure units in the process of risk pooling. Describe the effect of increasing the size of the risk pool on the mean loss of the pool and on the standard deviation of the mean loss in the pool. In your answer, assume that the losses of all the exposure units in the pool are independent and homogeneous.

Solution

a.

expected value of loss is $13,000

standard deviation of Rick’s losses is =Sqrt[670000000-(13,000)^2] =22383.029

b) The revised probability distribution is

c) Expected value of pooled mean is =26,000/2 =13,000

standard deviation is = sqrt[(419500000)-(13,000)^2]= 15827.18

d) There is no change in the pooled mean but the standard deviation of the pooled mean is decreased.

The standard deviation of pooled mean = standard deviation of unpooled mean/sqrt(n)