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  • 11. 2 - Key Properties of a Geometric Random Variable
    The variance of a geometric random variable \(X\) is: \(\sigma^2=Var(X)=\dfrac{1-p}{p^2}\) Proof To find the variance, we are going to use that trick of "adding zero" to the shortcut formula for the variance Recall that the shortcut formula is: \(\sigma^2=Var(X)=E(X^2)-[E(X)]^2\) We "add zero" by adding and subtracting \(E(X)\) to get:
  • Geometric Distribution - Formula, Mean (Expected Value), Variance
    Geometric Distribution represents the probability of getting the first success after repetitive failures Geometric distribution PMF is calculated by the formula P(X = x) = (1 - p)^(x-1) * p and geometric distribution CDF is calculated by the formula P(x ≤ x) = 1 - (1 - p)^x
  • Calculating the Variance of a Geometric Distribution - Study. com
    Learn how to calculate the variance of a geometric distribution, and see examples that walk through sample problems step-by-step, so that you can improve your statistics knowledge and
  • Geometric distribution (Expectation value, Variance, Example . . .
    The figure below describes the geometric distribution for $p=\frac{1}{2}$ (green)、 , $p=\frac{1}{4}$ (blue)、 $p=\frac{1}{8}$ (pink) The variance is、 \begin{eqnarray} V(X) = \left\{ \begin{array}{cc} 2 (p=\frac{1}{2}) \\ 12 (p=\frac{1}{4}) \\ 56 (p=\frac{1}{8}) \end{array} \right \end{eqnarray} The smaller $p$ is, the flatter the
  • Geometric Distribution | Formula, Mean and Examples
    Variance is a measure of dispersion that examines how far data in a distribution is spread out about the mean Var [X] = (1 - p) p2 The square root of the variance can be used to calculate the standard deviation The standard deviation also indicates how far the distribution deviates from the mean S D = √VAR [X] S D = √1 - p p
  • Variance in Geometric Distribution Calculator
    The formula to calculate the Variance in Geometric Distribution is: $$ \sigma^2 = \frac{1 - p}{p^2} $$





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