If X takes the values 1 and 3 with equal probability, which of the following is E[X]?

If X takes the values 1 and 3 with equal probability, which of the following is E[X]?

• A. Three
• B. One
• C. Four
• D. Two

Answer: (D)

Expected value is the probability-weighted average of all possible outcomes. For a discrete variable, E[X] = sum (value × its probability). Here, X can be 1 or 3, each with probability 1/2. So E[X] = 1×1/2 + 3×1/2 = (1 + 3)/2 = 2. This represents the long-run average you would expect if you could repeat the experiment many times. Therefore, the value is 2.

Expected value is the probability-weighted average of all possible outcomes. For a discrete variable, E[X] = sum (value × its probability).

Here, X can be 1 or 3, each with probability 1/2. So E[X] = 1×1/2 + 3×1/2 = (1 + 3)/2 = 2. This represents the long-run average you would expect if you could repeat the experiment many times. Therefore, the value is 2.