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

Question

x	P(x)
0	0.3
1	0.1
2	0.2
3	0.4

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

Answer 1

Here we go. In a textbook, some of the symbols are Greek. I will try to define the symbols I use. The expression for standard deviation of a probability distribution is

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 0.3 0 -1.7 2.89 0.867

1 0.1 0.1 -0.7 0.49 0.049

2 0.2 0.4 0.3 0.09 0.018

3 0.4 1.2 1.3 1.69 0.676

_____ _____

μ = Σ x P(x) = 1.7 AND σ² = Σ (x - μ)² P(x) = 1.61

σ² = the variance of the distribution. The standard deviation is the square root of that, or 1.269.