Question

x P(x) 0 0.25 1 0.3 2 0.1 3 0.35 Find the standard deviation of this probability distribution. Give your answer to at least 2 decimal places

Answer 1

Answer:

The standard deviation of this probability distribution is 1.2.

Step-by-step explanation:

We have that:

P(X = 0) = 0.25

P(X = 1) = 0.3

P(X = 2) = 0.1

P(X = 3) = 0.35

Mean:

Each value multiplied by its probability. So

$M = 0*0.25 + 1*0.3 + 2*0.1 + 3*0.35 = 1.55$

Variance:

Sum of the squares of the values subtracted from the mean, and multiplied by its probability.

$V = 0.25*(0-1.55)^2 + 0.3*(1-1.55)^2 + 0.1*(2-1.55)^2 + 0.35*(3-1.55)^2 = 1.4475$

Standard deviation:

Square root of the variance. So

$S = \sqrt{V} = \sqrt{1.4475} = 1.2$

The standard deviation of this probability distribution is 1.2.