The chi-square distribution is defined as the sum of squares of what kind of variables?

• A. Uniform
• B. Exponential
• C. Normal
• D. Binomial

Answer: (C)

The chi-square distribution comes from summing the squares of independent standard normal variables. If you take k independent standard normal variables (mean 0, variance 1), square each one, and add them up, you get a chi-square distribution with k degrees of freedom. Each squared normal term contributes one degree of freedom, so the number of terms controls the shape through the degrees of freedom. Other distributions like uniform, exponential, or binomial don’t form the chi-square in this way—the chi-square is a continuous distribution specifically tied to sums of squared normal variables.