Question

Calculate the standard deviation σ of X for the probability distribution. (Round your answer to two decimal places.) σ = x 1 2 3 4 P(X = x) 0.2 0.3 0.4 0.1

Answer 1

Solution :

Mean = = X * P(X)

= 1 *0.2 + 2 * 0.3 + 3 * 0.4 + 4 * 0.1

= ( 0.2+ 0.6+ 1.2+ 0.4)

= 2.4

Standard deviation =

=X 2 * P(X) - 2

=  [ 12 *0.2 + 22 * 0.3 + 32 * 0.4 + 42 * 0.1]-2.42

= [( 0.2+ 1.2 + 3.6 +1.6 ) )]-5.76

=6.6-5.76

=0.84

=0.92

Standard deviation = =0.92