Find the mean and standard deviation of the following probability distribution: `x_i :-3\ \ -1\ 0\ \ 1\ \ 3` `p_i :\ \ 0. 05\ \ 0. 45\ \ 0. 20\ \ 0. 25\ 0. 05`

Answer

Mean`=-0.2` and Standard Deviation`=1.25`

Explanation

The mean of the probability distribution is:


`Mean = E(X)=Sigma x_i cdot p_i`


`=-3 times 0.05+(-1) times 0.45+0 times 0.20+1 times 0.25+3 times 0.05`


`=-0.15-0.45+0+0.25+0.15=-0.20`


`rArr E(X)=-0.2`


Now,


`E(X^2)=Sigma x_i^2 times p_i`


`= (-3)^2 times 0.05+ (-1) ^2 times 0.45+ 0^2 times 0.20+ 1^2 times 0.25+3^2 times 0.05`


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