Find the mean and standard deviation of each of the following probability distribution: `x_i :1\ \ 3\ 4\ 5` `p_i : 0.4\ 0. 1\ 0. 2\ \ 0. 3`

Explanation

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

Standard Deviation is given by 5 D`=sqrt{ Variance } `where variance is given by:

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
...