Question

Calculate the mean and the standard deviation of this probability distribution.

X (Loss)	P(X)
$0	0.88
$100	0.05
$500	0.03
$1,000	0.02
$5,000	0.01
$10,000	0.007
$20,000	0.003

Answer 1

Solution:
Mean can be calculated as
Mean = summation(Xi*P(Xi))

X	P(X)	Xi*P(Xi)
0	0.88	0
100	0.05	5
500	0.03	15
1000	0.02	20
5000	0.01	50
10000	0.007	70
20000	0.003	60

Mean = 0 + 5+15+20+50+70+60 = 220
Standard deviation can be calculated as
Standard deviation = sqrt(Summation(Xi-mean)^2*P(Xi))

X	P(X)	Xi*P(Xi)	Xi-mean	(Xi-mean)^2	(Xi-mean)^2*P(Xi)
0	0.88	0	-220	48400	42592
100	0.05	5	-120	14400	720
500	0.03	15	280	78400	2352
1000	0.02	20	780	608400	12168
5000	0.01	50	4780	22848400	228484
10000	0.007	70	9780	95648400	669538.8
20000	0.003	60	19780	391248400	1173745.2

Standard deviation = sqrt(42592 + 720 + 2352 + 12168 + 228484 + 669538.8 + 1173745.2) = sqrt(2129600) = 1459.31