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
[tex]M = 0*0.25 + 1*0.3 + 2*0.1 + 3*0.35 = 1.55[/tex]
Variance:
Sum of the squares of the values subtracted from the mean, and multiplied by its probability.
[tex]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[/tex]
Standard deviation:
Square root of the variance. So
[tex]S = \sqrt{V} = \sqrt{1.4475} = 1.2[/tex]
The standard deviation of this probability distribution is 1.2.
