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--- b:head_first_statistics:using_the_normal_distribution [2025/10/26 23:19] – [Linear Transform] hkimscil
+++ b:head_first_statistics:using_the_normal_distribution [2025/10/29 02:12] (current) – [All aboard the Love Train] hkimscil
@@ Line 146: / Line 146: @@
 [1] 0.9406201
 > pnorm(-1.56, lower.tail = FALSE)
+[1] 0.9406201
+> pnorm(-1.56, 0, 1, lower.tail = F)
 [1] 0.9406201
 > pnorm(64, 71, sqrt(20.25), lower.tail = FALSE)
@@ Line 690: / Line 692: @@
 > pbinom(29,40, 1/4, lower.tail = F)
 [1] 4.630881e-11
+> dbinom(30:40,  40, 1/4)
+ [1] 4.140329e-11 4.451967e-12 4.173719e-13 3.372702e-14 2.314599e-15
+ [6] 1.322628e-16 6.123279e-18 2.206587e-19 5.806808e-21 9.926167e-23
+[11] 8.271806e-25
+> 1 - dbinom(0:29, 40, 1/4)
+ [1] 0.9999899 0.9998659 0.9991284 0.9963200 0.9886534 0.9727683
+ [7] 0.9470494 0.9142704 0.8821219 0.8602926 0.8556357 0.8687597
+[13] 0.8942786 0.9240975 0.9512055 0.9718076 0.9853165 0.9930901
+[19] 0.9970569 0.9988641 0.9996024 0.9998738 0.9999637 0.9999905
+[25] 0.9999978 0.9999995 0.9999999 1.0000000 1.0000000 1.0000000
+> sum(dbinom(30:40,  40, 1/4))
+[1] 4.630881e-11
+> 1 - sum(dbinom(0:29, 40, 1/4))
+[1] 4.630896e-11
+>
 </code>
@@ Line 812: / Line 830: @@
 <WRAP box>
-이를 R을 이용하여 구하면,
+위를 R에서 해보면
 <code>
-pbinom(5, 12, 1/2)
+> dbinom(0, 12, 1/2) + dbinom(1, 12, 1/2) + dbinom(2, 12, 1/2)
+>  + dbinom(3, 12, 1/2) + dbinom(4, 12, 1/2) + dbinom(5, 12, 1/2)
+[1] 0.387207
 </code>
+그러나, R에서는 더 간단한 방법으로
 <code>
 > pbinom(5, 12, 1/2)
@@ Line 822: / Line 842: @@
 </code>
-위는 아래와 같음을 이해해야 한다
+그리고, 위의 dbinom으로 하나씩 계산한다고 하더라도 아래처럼 하게 된다
 <code>
 > sum(dbinom(c(0:5),12,1/2))
@@ Line 909: / Line 929: @@
 <wrap #continuity_correction_egs />
 <WRAP box>
-X < 3  ----  <wrap spoiler> X < 2.5 </wrap>
+X < 3   <wrap spoiler> X < 2.5 </wrap>
-X > 3  ----  <wrap spoiler> X > 3.5 </wrap>
+X > 3   <wrap spoiler> X > 3.5 </wrap>
-X <_ 3  ----  <wrap spoiler> X < 3.5 </wrap>
+X <_ 3   <wrap spoiler> X < 3.5 </wrap>
-X >_ 3  ----  <wrap spoiler> X > 2.5 </wrap>
+X >_ 3   <wrap spoiler> X > 2.5 </wrap>
-<_ X < 10   ----  <wrap spoiler> 2.5 < X < 9.5 </wrap>
+<_ X < 10    <wrap spoiler> 2.5 < X < 9.5 </wrap>
-X = 0  ----  <wrap spoiler> -0.5 < X < 0.5 </wrap>
+X = 0   <wrap spoiler> -0.5 < X < 0.5 </wrap>
-<_ X <_ 10  ----  <wrap spoiler> 2.5 < X < 10.5 </wrap>
+<_ X <_ 10   <wrap spoiler> 2.5 < X < 10.5 </wrap>
-< X <_ 10  ----  <wrap spoiler> 3.5 < X < 10.5 </wrap>
+< X <_ 10   <wrap spoiler> 3.5 < X < 10.5 </wrap>
-X > 0  ----  <wrap spoiler> X > 0.5 </wrap>
+X > 0   <wrap spoiler> X > 0.5 </wrap>
-< X < 10  ----  <wrap spoiler> 3.5 < X < 9.5 </wrap>
+< X < 10   <wrap spoiler> 3.5 < X < 9.5 </wrap>
 </WRAP>
@@ Line 955: / Line 975: @@
 {{:b:head_first_statistics:pasted:20191118-113020.png}}
-$\lambda > 15$ 일 때, Poisson distribution, $X \sim Po(\lambda)$는 $X \sim N(\lambda, \lambda)$ 의 성격을 취한다.
+<fc #ff0000>$\lambda > 15$ 일 때,</fc> Poisson distribution, $X \sim Po(\lambda)$는 $X \sim N(\lambda, \lambda)$ 의 성격을 취한다.
 예)
@@ Line 1004: / Line 1024: @@
 $0.9654916 \sim 0.9656205$
+R에서 ppois을 이용하면
+<code>
+> ppois(51, 40)
+[1] 0.9612598
+>
+</code>
 ===== Check up =====