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--- b:head_first_statistics:geometric_distribution [2025/10/07 06:39] – [Proof of mean and variance of geometric distribution] hkimscil
+++ b:head_first_statistics:geometric_distribution [2025/10/07 06:39] (current) – [e.g.,] hkimscil
@@ Line 463: / Line 463: @@
   - The variance of the number of attempts.
 </WRAP>
+  - $P(X = 2) = p * q^{2-1}$
-$P(X = 2) = p * q^{2-1}$
+  - $P(X \le 4) = 1 - q^{4}$
-$P(X \le 4) = 1 - q^{4}$
+  - $P(X > 4) = q^{4}$
-$P(X > 4) = q^{4}$
+  - $E(X) = \displaystyle \frac{1}{p}$
-$E(X) = \displaystyle \frac{1}{p}$
+  - $Var(X) = \displaystyle \frac{q}{p^{2}}$
-$Var(X) = \displaystyle \frac{q}{p^{2}}$