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}

= [
0^{2 } * 0.05 +
1^{2} *0.20 + 2^{2} * 0.75] -1.7
^{2}

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

= 3.2 -2.89

=0.31

standard deviation=0.5568

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