Probability

Concept:The expected value of a discrete random variable is the sum of each outcome multiplied by its probability.Explanation:For a random variable $x$ taking values $x_1, x_2, x_3, x_4$ with probabilities $p_1, p_2, p_3, p_4$, the expected value is defined as:$$E(x) = x_1 p_1 + x_2 p_2 + x_3 p_3 + x_4 p_4$$Option C matches this definition: $p_1 x_1 + p_2 x_2 + p_3 x_3 + p_4 x_4$.Option B has mislabeled indices, and option A is just the sum of probabilities (which equals 1, not the expected value).Answer:The expected value of $x$ is $p_1 x_1 + p_2 x_2 + p_3 x_3 + p_4 x_4$.