Question

X P(x) 0 0.1 | 1 0.15 [2] 0.2 | 3 0.55 Find the standard deviation of this probability distribution. Give your answer to at least 2 decimal places Preview

Answer 1

Solution:
First we will calculate Expected mean whcih can be calculated as
Expected mean = $\sum$ (Xi*(P(Xi)) = 0*0.1 + 1*0.15 + 2*0.2 + 3*0.55 = 0+0.15+0.4+1.65 = 2.2

X	P(X)	X*P(X)
0	0.1	0
1	0.15	0.15
2	0.2	0.4
3	0.55	1.65

Standard deviation of Probability distribution cna be calculated as
Standard deviation = sqrt($\sum$((Xi-mean)^2 *P(Xi)) = sqrt((0-2.2)^2*0.1 + (1-2.2)^2*0.15 + (2-2.2)^2*0.2 + (3-2.2)^2*0.55)) = sqrt(0.484+0.216+0.008+0.352) = sqrt(1.06) = 1.03

X	P(X)	X*P(X)	(Xi-mean)	(Xi-mean)^2	(Xi-mean)^2*P(Xi)
0	0.1	0	-2.2	4.84	0.484
1	0.15	0.15	-1.2	1.44	0.216
2	0.2	0.4	-0.2	0.04	0.008
3	0.55	1.65	0.8	0.64	0.352