Question

Find the mean for the following probability distribution:

\[ \begin{array}{|c|c|c|c|c|} \hline x_i & 0 & 1 & 2 & 3 \\ \hline p_i & \frac{1}{8} & \frac{3}{8} & \frac{3}{8} & \frac{1}{8} \\ \hline \end{array} \]

Hint:

Mean of a discrete probability distribution is the sum of products of each value and its probability.

Answer 1

The mean \( \mu \) is given by: \[ \mu = \sum x_i p_i = 0 \times \frac{1}{8} + 1 \times \frac{3}{8} + 2 \times \frac{3}{8} + 3 \times \frac{1}{8} = 0 + \frac{3}{8} + \frac{6}{8} + \frac{3}{8} = \frac{12}{8} = \frac{3}{2} = 1.5. \]
Final answer: \[ \boxed{ \mu = 1.5. } \]