Please show your work. 3. A probability distribution for the claim sizes for an
ID: 3125896 • Letter: P
Question
Please show your work.
3. 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]?)
Explanation / Answer
Claim size Prob CDF x*p x^2*p 20 0.2 0.2 4 80 30 0.1 0.3 3 90 40 0.1 0.4 4 160 50 0.2 0.6 10 500 60 0.15 0.75 9 540 70 0.1 0.85 7 490 80 0.15 1 12 960 1 49 2820 Mean 49 Variance 2820-48^2 516 Std dev 22.71563 Within 1 std dev (26.284,71.716) Prob within 1std dev 0.85-0.2 0.65