Answer:
The standard deviation of the probability distribution is 1.02.
Step-by-step 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
[tex]E(X) = 0*0.1 +1*0.5 + 2*0.1 + 3*0.3 = 1.6[/tex]
Standard deviation:
[tex]\sqrt{V(X)} = \sqrt{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[/tex]
The standard deviation of the probability distribution is 1.02.
