http://www.commres.net/ 2026-04-17T08:25:35+00:00 http://www.commres.net/ http://www.commres.net/_media/wiki/logo.png text/html 2025-10-06T21:45:26+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.commres.net/b/head_first_statistics/binomial_distribution?rev=1759787126&do=diff Binomial Distribution * 1번의 시행에서 특정 사건 A가 발생할 확률을 p라고 하면 * n번의 (독립적인) 시행에서 사건 A가 발생할 때의 확률 분포를 * 이항확률분포라고 한다. 아래를 보면 * 각 한문제를 맞힐 확률은 1/4, 틀릴 확률은 3/4$$P(X = r) = {\huge\text{?} \cdot 0.25^{r} \cdot 0.75^{3-r}} $$$$P(X = r) = {\huge_{3}C_{r}} \cdot 0.25^{r} \cdot 0.75^{3-r}$$$_{n}C_{r}$$_{3}C_{1} = 3$\begin{eqnarray*} P(X = r) & = & _{3}C_{1} \cdot 0.25^{1} \cdot 0.75^{3-1} \\ & = & \frac{3!}{1! \cdot (3-1)!} \cdot 0.25 \cdot 0.75^2 \\ & = & 3 \cdot 0.25 \cdot 0.5625 \\ & = & 3 \cdot… text/html 2025-09-21T23:31:40+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.commres.net/b/head_first_statistics/calculating_probability?rev=1758497500&do=diff Calculating Probability How many pockets (holes) are there? 38 . . . * black = 18 blacks, consisted with * 8 odd numbers and * 10 even numbers * medium grey part = red, consisted with * 10 odd numbers and * 8 even numbers * white (almost) = green, consisted with$$P(A) = \frac {n(A)}{n(S)} $$$$ P(A) + P(A') = 1 $$$$ P(A') = 1 - P(A) $$$ P(9) $$ P(Green) $$ P(Black) $$ P(38) $\begin{eqnarray*} P(\text{Green}) & = & 2 / 38 \\ & = & 0.052632 & = & 0.053 \end{eqnarray*}\beg… text/html 2025-10-29T04:03:52+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.commres.net/b/head_first_statistics/constructing_confidence_intervals?rev=1761710632&do=diff Constructing Confidence Intervals Guessing with Confidence The problem with precision Point estimators are valuable, but they may give slight errors. Rather than specify an exact value, we can specify two values we expect flavor duration to lie between. $\Large{P(a < \mu < b) = 0.95} $\begin{eqnarray*} E(\overline{X}) & = & \mu \\ V(\overline{X}) & = & \dfrac{\sigma^{2}} {n} \\ \end{eqnarray*}$Var(\overline{X})$$s^{2}$\begin{eqnarray*} E(\overline{X}) & = & \mu \\ V(\overline{X}) & = & \… text/html 2023-12-13T04:33:15+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.commres.net/b/head_first_statistics/correlation_and_regression?rev=1702441995&do=diff Correlation and Regression: What's My Line? ---------- ---------- ---------- > s <- c(1.9,2.5,3.2,3.8,4.7,5.5, 5.9, 7.2) > c <- c(22,33,30,42,38,49,42,55) > plot(s,c) > df <- data.frame(s,c) > df s c 1 1.9 22 2 2.5 33 3 3.2 30 4 3.8 42 5 4.7 38 6 5.5 49 7 5.9 42 8 7.2 55 > plot(df) \begin{align} b = & \frac{\Sigma{(x-\overline{x})(y-\overline{y})}}{\Sigma{(x-\overline{x})^2}} \nonumber \\ = & \frac{SP}{SS_{x}} \\ a = & \overline{y} - b \; \overline{x} \;\;\; \because \; \o… text/html 2025-11-23T22:53:37+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.commres.net/b/head_first_statistics/estimating_populations_and_samples?rev=1763938417&do=diff Estimating Populations and Samples: Making Predictions So how can we use the results of the sample taste test to tell us the mean amount of time gumball flavor lasts for in the general gumball population? The answer is actually pretty intuitive. We assume that the mean flavor duration of the gumballs in the sample matches that of the population. In other words, we find the mean of the sample and use it as the mean for the population too.$$\mu \quad \quad \hat\mu$$$\hat\mu$$\hat{Y}$$\hat{\mu}… text/html 2025-10-14T23:31:02+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.commres.net/b/head_first_statistics/geometric_binomial_and_poisson_distributions?rev=1760484662&do=diff Geometric Binomial and Poisson Distributions 정리 기하분포, 이항분포, 포아송분포 \begin{align*} \text{Geometric Distribution: } \;\;\; \text{X} & \thicksim Geo(p) \\ p(X = k) & = q^{k-1} \cdot p \\ E\left[ X \right] & = \frac{1}{p} \\ V\left[ X \right] & = \frac{q}{p^2} \\ \\ \text{Binomial Distribution: } \;\;\; \text{X} & \thicksim B(n, p) \\ p(X = r) & = \binom{n}{r} \cdot p^{r} \cdot q^{n-r} \\ E\left[ X \right] & = {n}{p} \\ V\left[ X \right] & = {n}{p}{q} \\ \\ \text{Poisson Distribution: } \;\;\; \… text/html 2025-10-06T21:39:54+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.commres.net/b/head_first_statistics/geometric_distribution?rev=1759786794&do=diff Geometric Distribution 기하분포 \begin{align*} \text{Geometric Distribution: } \;\;\; \text{X} & \thicksim Geo(p) \\ p(X = k) & = q^{k-1} \cdot p \\ E\left[ X \right] & = \frac{1}{p} \\ V\left[ X \right] & = \frac{q}{p^2} \\ \\ \end{align*} Geometric Distributions The probability of Chad making a clear run down the slope is 0.2, and he's going to keep on trying until he succeeds. After he’s made his first successful run down the slopes, he’s going to stop snowboarding, and head back to the lodge… text/html 2025-09-16T22:07:25+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.commres.net/b/head_first_statistics/measuring_central_tendency?rev=1758060445&do=diff Measuring Central Tendency mean read mean document \begin{equation*} \text{Sum of all elements} = X_1 + X_2 + X_3 + X_4 + X_5 + . . . + X_n \\ \end{equation*} 위의 sum of all elements는 아래와 같이 표현된 수 있다. \begin{equation*} X_1 + X_2 + X_3 + X_4 + X_5 + . . . + X_n = \sum\limits_{i=1}^{n} X_i \end{equation*} 위의 sum of all elements를 n으로 나누는 것이 평균 \begin{equation*} \frac{\sum\limits_{i=1}^{n} X_i}{n} \end{equation*} 이것을 우리는 흔히 “무”라고 부른다. \begin{equation*} \mu = \frac{\sum\limits_{i=1}^{N} X_i}… text/html 2025-09-30T23:36:18+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.commres.net/b/head_first_statistics/permutation_and_combination?rev=1759275378&do=diff Permutation and Combination 순열과 조합 Permutation 세마리 말이 들어오는 순서의 경우의 수 So what if there are n horses? 팩토리얼 (n!) ---------- Arranging in a circle: 말한마리를 고정해 놓고 다른 말들을 배치한다고 할 때, 그 조합은? $$ \frac {n!} {p! * q!} $$$ {}{}_{n}\mathrm{P}_{r} $\begin{eqnarray*} _{3}P_{2} & = & \frac{3!}{(3-2)!} \\ & = & \frac {3!}{(3-2)!} = 6 \end{eqnarray*}\begin{eqnarray*} \text{Answer we want} & = & \frac {_{3}P_{2}}{2!} \\ \text{We call this} & = & _{3}C_{2} \\ _{3}C_{2} & = & \frac {\frac{3!}{(3-2)!}} {\… text/html 2025-10-06T23:42:27+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.commres.net/b/head_first_statistics/poisson_distribution?rev=1759794147&do=diff Poisson Distribution $$X \sim Po(\lambda)$$ 단위 시간, 단위 공간에 어떤 사건이 몇 번 발생할 것인가를 표현하는 이산 확률분포 모수(population parameter). * 단위시간 또는 단위공간에서 평균발생횟수 * lambda (λ)로 표시$\lambda$$$ P(X=r) = e^{- \lambda} \dfrac{\lambda^{r}} {r!},\qquad k = 0, 1, 2, . . ., $$\begin{eqnarray*} \sum_{r=0}^{\infty} e^{- \lambda} \dfrac{\lambda^{r}} {r!} & = & e^{- \lambda} \sum_{r=0}^{\infty} \dfrac{\lambda^{r}} {r!} \\ & = & e^{- \lambda} \left(1 + \lambda + \dfrac{\lambda^{2}}{2!} + \dfrac{\lambda^{3}}{3!} + . . . \… text/html 2025-09-24T22:04:24+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.commres.net/b/head_first_statistics/using_discrete_probability_distributions?rev=1758751464&do=diff using discrete probability distributions Dollar(D) Cherry(C) Lemon(L) Other(O) 0.1 0.2 0.2 0.5 * Probability of DDD * Probability of DDC (any order) * Probability of L * Probability of C * Probability of losing * P(D,D,D) = P(D) * P(D) * P(D)$$ E(X) = \sum{k * P(X=x)} $$$\sum = -0.77 $$$E(X) = -0.77$$$$E(X-\mu)^2 = \sum{(x-\mu)^2}*P(X=x) $$$$\mu = -.77 $$\begin{eqnarray*} \text{s} & = & \sqrt{s^2} \\ & = & \sqrt{2.6971} \\ & = & 1.642285 \\ \end{eqnarray*}$E(… text/html 2025-10-08T03:25:07+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.commres.net/b/head_first_statistics/using_hypothesis_tests?rev=1759893907&do=diff Look at the evidence Miracle drug: SnoreCull cures 90% of snores within 2 weeks. n = 15 Cured? Yes No Frequency 11 4 If the drug cures 90% of people, how many people in the sample of 15 snorers would you expect to have been cured? What sort of distribution do you think this follows?$H_{0}: P = .9$$H_{1}: P < .9 $$H_{1}: P \le .9 $$P(X \le 11)$$X \sim B(15, 0.9)$$P(X \le 11)$$X \sim B(15, 0.9)$$P(X \le 11)$$X \sim B(100, 0.9)$$P(X \le 80)$$X \sim N(\mu, \sigma^{2})$$\overline{X}$$… text/html 2025-10-08T03:16:38+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.commres.net/b/head_first_statistics/using_statistical_sampling?rev=1759893398&do=diff Using Statistical Sampling rnorm(16, 110, 10) A statistical population refers to the entire group of things that you're trying to measure, study, or analyze. It can refer to anything from humans to scores to gumballs. The key thing is that a population refers to all of them. A text/html 2025-10-29T02:12:59+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.commres.net/b/head_first_statistics/using_the_normal_distribution?rev=1761703979&do=diff Using the normal distribution 7장까지는 이산데이터에 (discrete data) 기초한 확률을 살펴보았다. 이산데이터란 정확한 가치에 기초한 것을 말하는 것으로 룰렛에서 이기는 횟수, 성공하는 횟수, 방문하는 횟수, 등등을 말한다. 비록 이는 종류로 측정된 것이 아닌 수치적데이터라고 할 수는 있지만, 연속적인 (continuous) 데이터와는 다른 성격을 갖는다. 끈의 길이나, IQ 점수, 성적(GPA), 등등은 단위적인 측정이 (discrete) 아닌, 정밀한 수치를 조밀하게 등분하여 측정하는 것을 말한다. \begin{eqnarray*} 1 & = & 20 * \text{height} \\ \text{height} & = & 1/20 \\ & = & 0.05 \end{eqnarray*}$P(X > 5)$\begin{eqnarray*} P(X > 5) & = & (20 - 5) * 0.05 \\ & = & 0.75 \end{eqnarray*}$$P(X <… text/html 2025-09-16T23:12:57+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.commres.net/b/head_first_statistics/variability_and_spread?rev=1758064377&do=diff Variability and Spread Who are you going to use for the upcoming game (basketball)? A 7 8 9 10 11 12 13 1 1 2 2 2 1 1 B 7 9 10 11 13 1 2 4 2 1 C 3 6 7 10 11 13 30 2 1 2 3 $ k(\frac{n}{100})$$ k(\frac{n}{100})$$ k(\frac{n}{100})$$ 20 * (10 /100) = 2 $$ \sum \text{deviation score}^2 = \sum \text{ds}^2 $$ \sum \text{error}^2 $$ \sum \text{random}^2 $$ \sum \text{residual}^2 $\begin{eqnarray*} \text{Individual score } … text/html 2025-09-07T23:22:22+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.commres.net/b/head_first_statistics/visualization?rev=1757287342&do=diff 정보의 시각화: 첫인상 * Charts * 모은 데이터를 분석하는 한 방법 * 상황을 파악하고 결론을 내려 결정을 (decision making) 할 수 있도록 한다. * 그러나, 데이터의 시각화에는 많은 허점이 따른다.