Multiple choice

A random variable X has its range $X = {3, 2, 1}$ with the probabilities, $\dfrac{1}{2},\dfrac{1}{3}$ and $\dfrac{1}{6}$ respectively. The mean value of X is

  1. $\dfrac{5}{3}$
  2. $\dfrac{7}{3}$
  3. $3$
  4. $4$
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B Correct answer
Explanation

The mean E(X) = sum(x * P(x)) = 3 * (1/2) + 2 * (1/3) + 1 * (1/6) = 3/2 + 2/3 + 1/6 = 9/6 + 4/6 + 1/6 = 14/6 = 7/3.

AI explanation

The expected value or mean of a random variable is the sum of its values multiplied by their corresponding probabilities. For this distribution, the mean equals 3*(1/2) + 2*(1/3) + 1*(1/6), which is 9/6 + 4/6 + 1/6. Adding these fractions gives a total of 14/6, which simplifies to 7/3.

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