Find the mean and standard deviation of the following probability distribution: `x_i :2\ \ 3\ \ 4` `p_i : 0.2\ \ 0. 5\ 0. 3`

Explanation

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

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

therefore, First we need 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:

` | x_(i) | p_(i) | x_(i)p_(i) | x_(i)^(2)p_(i) |
| :--- | :--- | :--- | :--- |
| 1 | 0.4 | 1xx0.4=0.4 | (1)^(2)xx0.4=0.4 |
| 2 | 0.3 | 2xx0.3=0.6 | 2^(2)xx0.3=1.2 |
...