Question

Consider the following probability distribution:

xi= 0, 1, 2, 3

P(X=xi)= 0.1, 0.1, 0.1, 0.7

The expected value and standard deviation is?

Answer #1

Solution :

Expected value E(x) = X * P(Xi)

= 0 * 0.1+ 1 *0.1 + 2 *0.1 + 3 *0.7

= ( 0+ 0.1 + 0.2+ 2.1)

E(x)= 2.4

Standard deviation =

=X 2 * P(Xi) - E(x) 2

= [ 02 *0.1+ 12 *0.1 + 22 *0.1 + 32 *0.7] -2.42

= [( 0+0.1 +0.4+6.3 ) )]-5.76

= 6.8-5.76

=1.04

=1.0198

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