In English this means you need to multiply each x value by the corresponding probability and get the sum of the results.
In English this means you need to do the following: Note: remember the standard deviation is the square root of the variance.
Example 1: Find the mean and variance of the following probability distribution.
To find the mean of the distribution we need to add another vertical column onto our table and a total row at the bottom of our table. and compute the x*P(x) for each x value then get the total of the column as our mean.
Thus the mean of example 1 is 1.7 .
To find the variance of the distribution we need to add 3 new vertical columns onto our original table and a total row at the bottom of the table. The computations in each of the new columns are as follows:
In the first new column, subtract the mean from each x value (remember our mean is 1.7 )
In the second new column, square each answer from the first new column.
In the third new column, multiply each answer from the second new column by each probability and finally get the sum of the answers from this step.

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