What is the weighted average of all possible values that the random variable can take, with the weights being the probabilities of those values?

What is the weighted average of all possible values that the random variable can take, with the weights being the probabilities of those values?

• A. Variance
• B. Expected value (or mean)
• C. Median
• D. Mode

Answer: (B)

The weighted average of all possible values with their probabilities is the expected value (mean). It’s found by summing each value times its probability: E[X] = Σ x_i P(X = x_i). This quantity represents the long-run average you’d expect if you could repeat the random process many times. For a discrete example like a six-sided die, each face is equally likely, so the expected value is (1+2+3+4+5+6)/6 = 3.5. This center measure differs from the median (the middle value) and the mode (the most probable value), and it’s also different from the variance, which measures spread rather than the central tendency.

The weighted average of all possible values with their probabilities is the expected value (mean). It’s found by summing each value times its probability: E[X] = Σ x_i P(X = x_i). This quantity represents the long-run average you’d expect if you could repeat the random process many times. For a discrete example like a six-sided die, each face is equally likely, so the expected value is (1+2+3+4+5+6)/6 = 3.5. This center measure differs from the median (the middle value) and the mode (the most probable value), and it’s also different from the variance, which measures spread rather than the central tendency.