Find the mean and standard deviation of the following probability distribution: `x_i :-5\ -4\ \ 1\ \ 2` `p_i :1/4\ \ 1/8\ \ 1/2\ 1/8`

Explanation

Mean of any probability distribution is given by Mean `=sum x_{i} P_{i}`

Variance `=sum x_{i}^{2} P_{i}-(sum x_{i} P_{i})^{2}`

therefore, first we have to find the products l.e. `{p}_{i} x_{i} and {p}_{i} {x}_{{i}}{ }^{2}` and add them to get mean and apply the above formula to get the variance.

Following table gives the required products:


`f{x}_{i} f{p}_{i} f{x}_{i} f{p}_{i} f{x}_{i}{ }^{2} f{p}_{i}
1 0.4 1 times 0.4=0.4 (1)^{2} times 0.4=0.4
2 0.3 2 times 0.3=0.6 2^{2} times 0.3=1.2
...