Question

An experiment has four outcomes with values and probability distribution give in the following table. i...

An experiment has four outcomes with values and probability distribution give in the following table.

i 1 2 3 4
Value xi 4 6 10 12
Probability Pr(xi) .1 .2 .3 .4

(a) What is the expected value?

(b) What is the standard deviation?

Math   Statistics-And-Probability   
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Answer #1

Solution :

x P(x) x * P(x) x2 * P(x)
4 0.1 0.4 1.6
6 0.2 1.2 7.2
10 0.3 3 30
12 0.4 4.8 57.6
Sum 1 9.4 96.4

(a) Expected value  = = X * P(X) = 9.4

Standard deviation =

=X 2 * P(X) - 2

=  96.4 - 9.42

= 2.8355

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