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--- b:head_first_statistics:geometric_distribution [2025/10/07 06:37] – [Expected value] hkimscil
+++ b:head_first_statistics:geometric_distribution [2025/10/07 06:39] (current) – [e.g.,] hkimscil
@@ Line 148: / Line 148: @@
 {{:b:head_first_statistics:pasted:20191031-005411.png}}
-===== Expected value =====
+====== Expected value ======
 X가 성공할 확률 p를 가진 Geometric distribution을 따른다  :: $X \sim \text{Geo}(p)$
@@ Line 452: / Line 452: @@
 ====== Proof of mean and variance of geometric distribution ======
 $(4)$, $(5)$에 대한 증명은 [[:Mean and Variance of Geometric Distribution]]
+===== e.g., =====
+<WRAP box>
+The probability that another snowboarder will make it down the slope without falling over is 0.4. Your job is to play like you’re the snowboarder and work out the following probabilities for your slope success.
+  - The probability that you will be successful on your second attempt, while failing on your first.
+  - The probability that you will be successful in 4 attempts or fewer.
+  - The probability that you will need more than 4 attempts to be successful.
+  - The number of attempts you expect you’ll need to make before being successful.
+  - The variance of the number of attempts.
+</WRAP>
+  - $P(X = 2) = p * q^{2-1}$
+  - $P(X \le 4) = 1 - q^{4}$
+  - $P(X > 4) = q^{4}$
+  - $E(X) = \displaystyle \frac{1}{p}$
+  - $Var(X) = \displaystyle \frac{q}{p^{2}}$