Question

Find the standard deviation of this probability distribution. Give your answer to at least 2 decimal placesx P(x)0 0.31 0.12 0.23 0.4

Answer 1

Complete Question

Find the standard deviation of this probability distribution. Give your answer to at least 2 decimal places

           x        1        2         3           4          5

         P(x)      0     0.31     0.12     0.23       0.4

Answer:

The value is  $\sigma = 0.89$

Step-by-step explanation:

From the question we are told that

  The probability distribution is  

           x        1        2         3           4          5

         P(x)      0     0.31     0.12     0.23       0.4

So

           $x^2$     1           4         9          16           25  

Generally the mean is mathematically represented as

            $E(X) = \sum [x * P(x)]$

=>         $E(X) = (1 * 0) + (2 * 0.31 ) + (3 * 0.12 ) + (4 * 0.23) + (5 * 0.4 )$

=>         $E(X) = 3.9$

Generally  

      $E(X^2) = \sum [X^2 * P(x)]$

=>   $E(X^2) = (1 * 0) + (4 * 0.31 ) + (9 * 0.12) + (16 * 0.23) + (25 * 0.4)$

=>   $E(X^2) =16$

Generally the variance of this probability distribution is

      $V(X) = E(X^2) - [E(X)]^2$

     $V(X) = 16 - 3.9^2$

    $V(X) = 0.79$

Generally the standard deviation of this probability distribution is  

       $\sigma = \sqrt{V(x)}$

=>    $\sigma = \sqrt{0.79}$

=>    $\sigma = 0.889$