Question

Consider the probability distribution shown below.

x 0 1 2

P(x) 0.05 0.20 0.75

Compute the expected value of the distribution.

Compute the standard deviation of the distribution. (Round your answer to four decimal places.)

Answer 1

Solution :

expected value = = X * P(X)

= 0 *0.05 + 1 *0.20 + 2 *0.75  

= (0 + 0.20 + 1.5 )

expected value = 1.7

Standard deviation =

=X ² * P(X) - ²

=  [ 0²   * 0.05 + 1²   *0.20 + 2² * 0.75] -1.7 ²

= [( 0+ 0.20 + 3 ) )] -2.89

= 3.2 -2.89

=0.31

standard deviation=0.5568