Question

PRACTICE ANOTHER Calculate the standard deviation σ of X for the probability distribution. (Round your answer to two decimal places.) σ = (No Response) 1.00

Answer 1

Complete  Question

The complete question is shown on the first uploaded image

Answer:

The standard deviation is  $\sigma = 1.17$      

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

           $\sigma = \sqrt{ \sum x^2 P(x) - (\sum x P(x))^2 }$

Here    $x^2 = 1^2 \ \ 2^2 \ \ 3 ^2 \ \ 4^2$

    =>     $x^2 = 1 \ \ 4 \ \ 9\ 16$

      $\sum x^2 * P(x) = (1 * 0.2) + (4 * 0.2 ) + (9 * 0.2 ) + (16 * 0.2 )$

     $\sum x^2 * P(x) = 9.4$

      $\sum x P(x) = (1 *0.2) + (2*0.2) + (3 * 0.2) + (4 * 0.2)$

     $\sum x P(x) = 2.8$

So  

    $\sigma = \sqrt{ 9.2 - (2.8)^2 }$            

    $\sigma = 1.17$