Complete Question
The complete question is shown on the first uploaded image
Answer:
The standard deviation is [tex]\sigma = 1.17[/tex]
Step-by-step explanation:
From the question we are told that
The data is
x 1 2 3 4
P(X = x) 0.2 0.2 0.2 0.4
Generally the standard deviation is mathematically represented as
[tex]\sigma = \sqrt{ \sum x^2 P(x) - (\sum x P(x))^2 }[/tex]
Here [tex]x^2 = 1^2 \ \ 2^2 \ \ 3 ^2 \ \ 4^2[/tex]
=> [tex]x^2 = 1 \ \ 4 \ \ 9\ 16 \[/tex]
[tex]\sum x^2 * P(x) = (1 * 0.2) + (4 * 0.2 ) + (9 * 0.2 ) + (16 * 0.2 )[/tex]
[tex]\sum x^2 * P(x) = 9.4[/tex]
[tex]\sum x P(x) = (1 *0.2) + (2*0.2) + (3 * 0.2) + (4 * 0.2)[/tex]
[tex]\sum x P(x) = 2.8[/tex]
So
[tex]\sigma = \sqrt{ 9.2 - (2.8)^2 }[/tex]
[tex]\sigma = 1.17[/tex]
