Find the standard deviation of this probability distribution. Give your answer to at least 2 decimal places

Question

x	P(x)
0	0.05
1	0.05
2	0.2
3	0.7

Find the standard deviation of this probability distribution. Give your answer to at least 2 decimal places

Answer 1

σ = √ (∑ (x - μ)² P(x) ]

where μ = Σ x P(x), and x are the values which have probability assigned by P(x). This is best done with a table.

x | P(x) | x [P(x)] | x - μ | (x - μ)² | (x - μ)² P(x)

0 | 0.05 | 0 | -2.55 | 6.50 | 0.325

1 | 0.05 | 0.05 | -1.55 | 2.40 | 0.120

2 | 0.2 | 0.4 | -0.55 | 0.30 | 0.060

3 | 0.7 | 2.1 | 0.45 | 0.20 | 0.140

_____ _____

μ = Σ x P(x) = 2.55 AND σ² = Σ (x - μ)² P(x) = 0.645