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--- b:head_first_statistics:geometric_binomial_and_poisson_distributions [2025/10/12 23:49] – [e.g.,] hkimscil
+++ b:head_first_statistics:geometric_binomial_and_poisson_distributions [2025/10/14 23:31] (current) – [e.g.,] hkimscil
@@ Line 740: / Line 740: @@
 <code>
+> p <- .4
+> q <- 1-p
+>
 > p*q^(2-1)
 [1] 0.24
@@ Line 758: / Line 761: @@
 > 1-sum(dgeom(0:3, p))
 [1] 0.1296
->
+> 1-pgeom(3, p)
+[1] 0.1296
+> pgeom(3, p, lower.tail = F)
+[1] 0.1296
+>
 > 1/p
 [1] 2.5
@@ Line 815: / Line 822: @@
 \begin{eqnarray*}
 P(X = r) & = & _{n}C_{r} \cdot p^{r} \cdot q^{n-r} \;\;\; \text{Where,} \\
-_{n}C_{r} & = & \frac {n!}{r!(n-r)!}
+\displaystyle _{n}C_{r} & = & \displaystyle \dfrac {n!}{r!(n-r)!} \\
+\text{c.f.,  } \\
+\displaystyle _{n} P_{r} & = & \displaystyle \dfrac {n!} {(n-r)!} \\
 \end{eqnarray*}
+see [[:b:head_first_statistics:permutation_and_combination#what_if_horse_order_doesn_t_matter|Permutation chapter]]
 p = 각 시행에서 성공할 확률
@@ Line 910: / Line 922: @@
 dbinom(r, n, p)
+# dbinom(2, 5, 1/4)
 </code>
@@ Line 932: / Line 945: @@
 >
 </code>
 Ans 2.
@@ Line 1056: / Line 1064: @@
 n <- 6
 pbinom(5, n, p)
 - dbinom(6, n, p)
+sum(dbinom(0:5, n, p))
 </code>
 <code>
@@ Line 1067: / Line 1075: @@
 > 1 - dbinom(6, n, p)
 [1] 0.9997559
+> sum(dbinom(0:5, n, p))
+[1] 0.9997559
+>
 </code>