Answer:
The standard deviation of the probability distribution is 0.79
Step-by-step explanation:
We are given the following in the question:
x: 0 1 2 3
P(x): 0.46 0.41 0.09 0.04
We have to find the standard deviation of the probability distribution.
Formula:
[tex]\frac{x}{y} E(x) = \displaystyle\sum x_iP(x_i)\\E(x) = 0(0.46 ) + 1(0.41)+2(0.09 )+3 (0.04)\\E(x) = 0.71\\E(x^2) = \sum x_i^2p(X_i)\\E(x^2) =0^2(0.46 ) + 1^2(0.41)+2^2(0.09 )+3^2 (0.04)\\E(x^2)= 1.13\\\sigma^2 = E(x^2) - (E(x))^2\\\sigma^2 = 1.13 - (0.71)^2 = 0.6259\\\sigma = \sqrt{0.6259} = 0.79[/tex]
Thus, the standard deviation of the probability distribution is 0.7911
