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.

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.

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.