A probability distribution for the claim sizes for an auto insurance policy is given in the table below
|
Claim Size
|
Probability
|
|
20
|
0.20
|
|
30
|
0.10
|
|
40
|
0.10
|
|
50
|
0.20
|
|
60
|
0.15
|
|
70
|
0.10
|
|
80
|
0.15
|
a) Evaluate the cdf for this distribution at the following points: 0, 20, 30, 40, 50, 90.
b.) What is the mean of this distribution?
c.) What is the variance of this distribution?
d.) What percentage of the claims are within one standard deviation of the mean claim size? (In other words, what percentage of the claims are greater than or equal to [the mean size minus one standard deviation] but less than or equal to [the mean size plus one standard deviation]?)