Chi-Square Distribution Calculator

Definition: The chi-square distribution is a probability distribution of a sum of squared standard normal random variables. It is widely used in statistical inference, particularly for tests of independence and goodness-of-fit tests.

• Mean: $E(X) = k$ (equals degrees of freedom)
• Variance: $\text{Var}(X) = 2k$
• Mode: $\max(k-2, 0)$
• Support: $(0, \infty)$
• Special cases:
  • The sum of $k$ standard normal variables squared
  • $\chi^2_1$ is the square of a standard normal
  • For large $k$, approaches normal distribution