Question

Distribution A: xi Distribution A: P(X=xi) Distribution B: xi Distribution B: P(X=xi) 0 0.03 0 0.49 1 0.08 1 0.23 2 0.17 2 0.17 3 0.23 3 0.08 4 0.49 4 0.03 What is the standard deviation for distribution​ B?

What is the standard deviation for distribution​ B?

0   0.49

1   0.23

2 0.17

3 0.08

4 0.03

Answer 1

Answer :

Given data is :

Distribution B is :

X	0	1	2	3	4
P(X = x)	0.49	0.23	0.17	0.08	0.03

E(X) =

= [(0 * 0.49) + (1 * 0.23) + (2 * 0.17) + (3 * 0.08) + (4 * 0.03)]

= [ 0 + 0.23 + 0.34 + 0.24 + 0.12]

= 0.93

E(X) = 0.93

therefore,

standard deviation =

where

=

= [0 + 0.23 + (4 * 0.17) + (9 * 0.08) + (16 * 0.03)]

= 0 + 0.23 + 0.68 + 0.72 + 0.48

= 2.11

so,

standard deviation =

=

=

=

=

Standard deviation for distribution B = 1.116