Find the mean of the following probability distribution:

X = x_i : 1 2 3

P (X = x_i) : $\frac{1}{4}$ $\frac{1}{8}$ $\frac{5}{8}$

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Solution

x_i p_i p_ix_i

1 $\frac{1}{4}$ $\frac{1}{4}$

2 $\frac{1}{8}$ $\frac{2}{8}$

3 $\frac{5}{8}$ $\frac{15}{8}$

Mean = $\sum_{}^{}$ p_ix_i = $\frac{1}{4} + \frac{2}{8} + \frac{15}{8} = \frac{2 + 2 + 15}{8} = \frac{19}{8}$

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X = x_i :	1	2	3
P (X = x_i) :	$\frac{1}{4}$	$\frac{1}{8}$	$\frac{5}{8}$