Variance

• How to Find the Mean and Variance of an Exponential Distribution
  For an exponential distribution with rate λ, the mean is 1/λ and the variance is 1/λ²; see the derivation and scale-parameter version.
• Mean and Variance of the Weibull Distribution
  For a Weibull distribution with shape k and scale λ, the mean is λΓ(1+1/k) and the variance is λ²[Γ(1+2/k)−Γ(1+1/k)²].
• How to Prove the Variance of a Geometric Distribution
  Derive Var(X) = (1-p)/p² for a geometric random variable using its probability-generating function, and see how the 0-based convention differs.
• How Do You Sum a Random Number of Independent Variables?
  For an independent random count and iid summands, derive the random sum’s mean and variance, see a worked example, and learn when the formulas fail.
• Does Standard Deviation Change When You Add or Multiply by a Constant?
  Adding a constant leaves the standard deviation unchanged; multiplying by a scales it by |a| and the variance by a². Proof, examples and the general rule for aX + b.
• What Is the Standard Deviation of a Dice Roll?
  The standard deviation of one fair six-sided die is √(35/12) ≈ 1.708. See the derivation, the formula for any die, and how it scales for sums and averages.