Find the mean of the following probability distribution: `X=x_i :\ \ 1 \ \ 2 \ \ 3` `\ P(X=x_i):1/4 \ \ 1/8 \ \ 5/8 \ \ ` .

Explanation

To find the mean of the given probability distribution, we can follow these steps:

### Step 1: Identify the values of X and their corresponding probabilities
We have:
- \( X = 1 \) with \( P(X=1) = \frac{1}{4} \)
- \( X = 2 \) with \( P(X=2) = \frac{1}{8} \)
- \( X = 3 \) with \( P(X=3) = \frac{5}{8} \)

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