Differences

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--- binomial_distribution [2019/11/04 15:28] – hkimscil
+++ binomial_distribution [2020/11/27 19:42] (current) – hkimscil
@@ Line 1: / Line 1: @@
 ====== Binomial Distribution ======
+  - 1번의 시행에서 특정 사건 A가 발생할 확률을 p라고 하면
+  - n번의 (독립적인) 시행에서 사건 A가 발생할 때의 확률 분포를
+  - 이항확률분포라고 한다.
 \begin{eqnarray*}
@@ Line 7: / Line 10: @@
 **The number of successes in n independent Bernoulli trials has a binomial distribution.**
-n independent Bernoulli trials
+이는 n 번의 독립적인 Bernoulli trials 로 볼 수 있다.
   * There are n independent trials
   * Each trial can result in one of two possible outcomes, labelled success and failure.
@@ Line 14: / Line 17: @@
   * P(failure) = 1-p
-\begin{eqnarray*}
+일반적으로 binomial distribution은 아래와 같이 계산된다.
-P(X=x) = _{n}C_{x} \cdot p^{x} \cdot (1-p)^{n-x}, \;\; \text{for} \;\; x = 0, 1, 2, . . ., n. \\
-\end{eqnarray*}
+\begin{align*}
+P(X=x) & = _{n}C_{x} \cdot p^{x} \cdot (1-p)^{n-x}, \;\; \text{for} \;\; x = 0, 1, 2, . . ., n. \\
+\text{or } & \\
+P(X=x) & = {{n} \choose {x}} \cdot p^{x} \cdot (1-p)^{n-x}, \;\; \text{for} \;\; x = 0, 1, 2, . . ., n. \\
+\end{align*}
 A balanced dice is rolled 3 times. What is probability a 5 comes up exactly twice?
@@ Line 25: / Line 32: @@
 \begin{eqnarray*}
-P(X=2) & = & {{3} \choose {2}} (\frac{1}{6})^{2} (\frac{5}{6})^{3-2} \\
+P(X=2) & = & {{3} \choose {2}} \left(\frac{1}{6}\right)^{2} \left(\frac{5}{6}\right)^{3-2} \\
 & = & 0.0694
 \end{eqnarray*}