Compute the expected value E[X] for a discrete random variable X taking values 1, 2, 3 with probabilities 0.2, 0.5, 0.3.

• A. 1.8
• B. 2.1
• C. 2.4
• D. 2.0

Answer: (B)

The expected value is the weighted average of the possible values, using their probabilities as weights. For X taking 1, 2, and 3 with probabilities 0.2, 0.5, and 0.3, multiply each value by its probability and add them up: 1×0.2 = 0.2, 2×0.5 = 1.0, 3×0.3 = 0.9. Sum = 0.2 + 1.0 + 0.9 = 2.1. So the expected value is 2.1. The other numbers would come from different data or arithmetic errors, but with the given probabilities, 2.1 is the correct weighted average.