Question

Calculate the standard deviation of X for the probability distribution. (Round your answer to two decimal places.)

x 0 1 2 3
P(X = x) 0.1 0.5 0.1 0.3

Answer 1

The standard deviation of the probability distribution is 1.02.

Explanation:

Standard deviation of the distribution:

Square root of the sum of the difference squared between each value and the mean multiplied by its probability.

Mean:

Each value multiplied by its probability. So

`E(X) = 0*0.1 +1*0.5 + 2*0.1 + 3*0.3 = 1.6`

Standard deviation:

`√(V(X)) = √(0.1*(0-1.6)^2 + 0.5*(1-1.6)^2 + 0.1*(2-1.6)^2 + 0.3*(3-1.6)^2) = 1.02`

The standard deviation of the probability distribution is 1.02.