compute the mean and variance of the following probability distribution

x P(x)

6 0.1

12 0.35

18 0.25

24 0.30

24

0.30

The mean can be calculated by:

- For each [x,P(x)] pair, multiply them together

- Sum all of these values

This gives you:

0.6 + 4.2 + 4.5 + 7.2

= 16.5

And the standard deviation can be calculated by:

- For each [x,P(x)] pair, multiply (x-mean)^2 by P(x)

- Sum all these values and take the square root

= (11.025 + 7.0875 + 0.5625 + 16.875)^0.5

= 5.9624

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