If X is a random variable which can only assume the value x, then you have
\mathbb{E}(X)=\mu = x
This makes sense, since X assumes only one value, and so "on average" it assumes that value as well. Think for example that X equals constantly 3. Then you sample, for example, ten values from X, and you will have x_1 = 3, x_2 = 3, ... , x_10=3, since you can't have anything but 3. Now, compute the average:
\mu = \frac{x_1 + ... + x_10}{10} = \frac{3+...+3}{10} = \frac{10\cdot 3}{10} = 3
To be more precise, you may use the definition
\mathbb{E}(X) = \sum p_i x_i
i.e. the weighted sum of all possible values, weighted with their probabilities. Since X only assumes the value x with probability 1, you have
\mathbb{E}(X) = \sum p_i x_i = 1\cdot x = x
