Answer:
The standard deviation of X is 0.7
Step-by-step explanation:
We are given the following distribution:
x: 0 1 2 3
P(x): 0.3 0.5 0.2 0.4
We have to find the standard deviation of X.
Formula:
[tex]E(x) = \displaystyle\sum x_iP(x_i)\\\\E(x) =0(0.3) + 1(0.5) + 2(0.2) + 3(0.4)\\\\E(x) = 2.1\\\\E(x^2) = \displaystyle\sum x_i^2P(x_i)\\\\E(x^2) =0(0.3) + 1(0.5) + 4(0.2) + 9(0.4)\\\\E(x^2) = 4.9\\\\Var(x) = E(x^2) - (E(x))^2 = 4.9-(2.1)^2 = 0.49\\\\\sigma(x) = \sqrt{Var(x)} =\sqrt{0.49} = 0.7[/tex]
Thus, the standard deviation of X is 0.7
