Student's t-Distribution Calculator

Definition: The Student's t-distribution is a continuous probability distribution that arises when estimating the mean of a normally distributed population in situations where the sample size is small and the population standard deviation is unknown.

• Mean: $E(X) = 0$ for $\nu > 1$
• Variance: $\text{Var}(X) = \frac{\nu}{\nu-2}$ for $\nu > 2$
• Key Characteristics:
  • Bell-shaped and symmetric about 0
  • More peaked and heavier tails than normal distribution
  • Approaches normal distribution as ν increases
  • Support is all real numbers