Find the mean and standard deviation of the following probability distribution: `x_i :\ \ 1\ \ 2 \ \ 3\ \ 4` `p_i :\ \ 0. 4\ \ 0. 3\ \ 0. 2\ \ 0. 1`

Answer

Mean`=5` and Standard Deviation`=1`

Explanation

The mean of the probability distribution is:


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


`=1 times 0.4+2 times 0.3+3 times 0.2+4 times 0.1`


`=0.4+0.6+0.6+0.4=2`


`rArr E(X)=2`


Now,


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


`= 1^2 times 0.4+ 2 ^2 times 0.3+ 3^2 times 0.2+ 4^2 times 0.1`


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