Find the mean and standard deviation of the following probability distribution: `x_i :0 \ \ 1 \ \ 2 \ \ 3 \ \ 4 \ \ 5` `p_i :1/6 \ \ 5/(18) \ \ 2/9 \ \ 1/6 \ \ 1/9 \ \ 1/(18)`

Answer

Mean`=1.94` and Standard Deviation`=1.62`

Explanation

The mean of the probability distribution is:


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


`=0 times 1/6+1 times 5/18+2 times 2/9+3 times 1/6+4 times 1/9+5 times 1/18`


`=0+5/18+4/9+1/2+4/9+5/18=1/18[5+8+9+8+5]=35/18=1.94`


`rArr E(X)=1.94`


Now,


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


`= 0^2 times 1/6+ 1 ^2 times 5/18+ 2^2 times 2/9+ 3^2 times 1/6+4^2 times 1/9+5^2 times 1/18`


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