Moments of a die roll

Computing moments of a discrete uniform distribution

This is a foundational probability question that tests your ability to compute the first and second moments of a simple discrete distribution. It is a building block for understanding variance, risk measures, and more complex stochastic problems in quantitative finance.

To solve problems of this type, you need to apply the definition of expectation to a finite discrete distribution, carefully sum the weighted outcomes, and simplify your result to lowest terms. This is essential practice because moments appear constantly in portfolio theory, option pricing, and risk management—any misstep in the arithmetic compounds downstream.

• Definition of expectation for discrete random variables
• Symmetry and simplification in uniform distributions
• Fraction arithmetic and reduction