xi 
0 1 2 3 

P(X = xi) 
0.20 0.30 0.40 0.10 
What is the standard deviation of X?
A 
0.840 

B 
0.090 

C 
1.345 

D 
0.917 
Solution:
x  P(x)  x * P(x)  x2 * P(x) 
0  0.2  0  0 
1  0.3  0.3  0.3 
2  0.4  0.8  1.6 
3  0.1  0.3  0.9 
Sum  1  1.4  2.8 
Mean = X * P(X)
= 1.4
Standard deviation =
=X 2 * P(X)  2
= 2.8  (1.4)2 = 0.84
Standard deviation = = 0.917
option D is correct
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