A four‑sided die, also called a tetrahedral die, has faces numbered 1 through 4. Each face is equally likely, giving a uniform probability distribution (P(X = x) = frac{1}{4}) for (x in {1,2,3,4}).
The expected value of a single roll is calculated by summing each outcome multiplied by its probability. This yields (E = frac{1+2+3+4}{4} = 2.5). The variance, a measure of spread, is (Var = frac{(1-2.5)^2+(2-2.5)^2+(3-2.5)^2+(4-2.5)^2}{4} = 1.25).
When rolling multiple dice, the total sum follows a discrete convolution of the single‑die distribution. Simulating many trials quickly approximates the theoretical distribution, which is useful in game design, probability teaching, and Monte‑Carlo methods.
What is the expected value of a single roll of a four-sided die?
How do I calculate the variance for a four-sided die?
What does each face of a four-sided die represent?
Can you explain the concept of uniform probability distribution in this context?
How does rolling multiple four-sided dice affect the expected value and variance?
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