Question

2.The random variable X has the probability distribution table shown below. Calculate the standard deviation rounded to the four decimal places.

x −1 0 4 10

P(X = x) 0.2 0.3 0.3 0.2

Answer 1

Solution :

Mean = = X * P(X)

= -1 * 0.2 + 0 *0.3 +4 *0.3 + 10*0.2

= ( - 0.2+ 0+ 1.2 +2 )

= 3

Standard deviation =

=X 2 * P(X) - 2

=  [ -12 * 0.2 + 02 *0.3 +4 2*0.3 + 102*0.2]-32

= [( -0.2+ 0 +4.8 +20 ) )]-9

= 24.6-9

=15.6

=3.9497

Standard deviation = =3.9497