# User:Gesalbte

User:Arknascar44/Love Cabal

Welcome to Wikimedia Commons, Gesalbte!

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## Introduction

Born into Uncyclopedia, this user is an extraordinary dumbfuck[1], who has messed up everybody in Spring Weekend[2].
This user is currently a student studying finance in college and enjoys the sunshine, rain, and forest of Connecticut. If you have to excuse him, please leave message in the discussion page.
This user is a dumbfuck writer[3] and wrote a lot of stuff that appreciated by his professor[4]. For example, the sentence below comes from Nostra Via in Regnum Ducit:

 “ Only after thou hast suffered the darkened night, there cometh the light. ”

## Statistics

### Chapter 2

inter-quartile range (IQR; 四分位距); Outlier: |z|＞2; ext: |z|＞3
Chebychev’s Theorem: at least data is within ( ), Empirical Rule: approx. 68% at z ∈ (-1s, 1s), approx. 95% at z ∈ (-2s, 2s), approx. 99.7% at z ∈ (-3s, 3s)

### Chapter 3

```: from n choose (组合) k;  : from n permute (排列) k.
```
intersection,  : union, Ac: complementary.  ; factorials (n!);

### Chapter 4

Discrete random variables (rv); STAT → CALC → 1-Var Stats → L1(值), L2(个数)

Binomial r.v. (二项分布; Bernoulli trial: coin-toss); =math. expectation=np,
Probability Density Function: ; DISTR → binompdf (n, p, k). [n个成功率为p的伯努利实验，成功k次的概率是多少？] Cumulative Distribution Function: DISTR → binomcdf (n, p, k) [n个成功率为p的伯努利实验，至少成功k次的概率是多少？]
Uniform (平均) distribution:  ;  ;  ; .
Normal distribution (正态分布): Z ~ N (), ~ N (0, 1); std. norm.: N (0, 1);
Cumulative Distribution Function: DISTR → normalcdf (a, b, μ, σ). [对于正态分布N ()，作下限为a，上限为b的定积分得多少？] Quantile function: DISTR → invnorm (p, μ, σ). [对于正态分布N ()，作积分下限为-∞的定积分得p时，积分上限是多少？]
Criteria for determining whether normal distribution: 1) histogram or stem and leaf display is bell shaped; 2) data satisfies empirical rule; 3) IQR/s = (Q3-Q1)/s is approximately 1.3; 4) a normal probability plot is approximately linear. [TI: 1) clear y functions 2) enter data 3) 2ND → Y= → ... → 6th plot, x axis 4) ZOOM 9]
Central Limit Theorem: 许多(n>30)平均值标准差的分布，其平均值的分布为N (, ).
Chapter 5: Jargon Box: confidence coefficient(置信系数; 1-α), confidence level(置信度; 100×(1-α)).
A. 根据样本猜总体的平均值μ: = , where = invT(1-/2, n-1), n-1是自由度.
Also that T-distribution function (normal + centered at 0, fatter tails; df = n-1↑tend to be normal). Std. dev. of T-distribution is , its Cumulative Distribution Function: DISTR → tcdf(a, b, df), where df=n-1 [对于自由度df的T分布，作下限为a，上限为b的定积分得多少？]; its Quantile function: DISTR → invT(p, df) [对于自由度为df的T分布，作积分下限为-∞的定积分得p时，积分上限是多少？].

where = invNorm(1-/2), 1-/2 = (1-CC)/2. [ = 1.645; = 1.960; = 2.576]

B. 根据样本的比例猜总体的比例p: p , when we have large samples ( , ), there , . This function is based on  ; , where .
When p nears 0 or 1, use adjusted confidence interval , where . Sampling error (SE; SE=.5Width) or margin of error (ME): , therefore .

### Chapter 6

Hypothesis testing [无论如何，总体分布必须为正态的时候才能检定]
Type I error: rejected a correct H0; Type II error: failed to reject a wrong H0. The smaller
selected, the more evidence (larger z) needed to reject H0. 思想罪: 思想就是犯罪！[5]
A. t-test: H0说μ0, 你不相信, 就搞了Ha: , s, n, 代入下面这个公式, 看看你的图像牛逼不？

where is the sample mean, μ0 is the claimed mean (=H0), s is sample std.dev.

Left tailed test: Ha: μ < μ0; reject H0 if t < -t = -invT(1-α, n-1); p-value = tcdf(-10^99, t, n-1). Two tailed test: Ha: μ ≠ μ0; reject H0 if t [-t, t], where t = invT(1-α/2, n-1); p-value = 2×tcdf(|t|, 10^99, n-1). Right tailed test: Ha: μ > μ0; reject H0 if t > t = invT(1-α, n-1); p-value = tcdf(t, 10^99, n-1).

where is the sample mean, μ0 is the claimed mean (=H0), σ is population std.dev.

Left tailed test: Ha: μ < μ0; reject H0 if z < -z = -invNorm(1-α); p-value = normalcdf(-10^99, z). Two tailed test: Ha: μ ≠ μ0; reject H0 if z [-z, z], where z = invNorm(1-α/2); p-value = 2×normalcdf(|z|, 10^99). Right tailed test: Ha: μ > μ0; reject H0 if z > z = invNorm(1-α); p-value = normalcdf(z, 10^99).
B. z-test for population proportion:  ; .

where is sample proportion, p0 is the claimed mean proportion (=H0).

Left tailed test: Ha: p < p 0; reject H0 if z < -z = -invNorm(1-α); p-value = normalcdf(-10^99, z). Two tailed test: Ha: p ≠ p0; reject H0 if z [-z, z], where z = invNorm(1-α/2); p-value = 2×normalcdf(|z|, 10^99). Right tailed test: Ha: p > p 0; reject H0 if z > z = invNorm(1-α); p-value = normalcdf(z, 10^99).

### Chapter 7

```Large sample: CI = ;                 Test statistic:
```

One tailed test:
H0: (μ1-μ2) = D0
Ha: (μ1-μ2) < D0
[or Ha: (μ1-μ2) > D0]
Two tailed test:
H0: (μ1-μ2) = D0
Ha: (μ1-μ2) ≠ D0

where D0 = hypothesized difference between the means (often it is equal to 0)

```
```

Rejection region: z < -
[or z > ]
Rejection region: |z| >

t-test: CI = , where , = invT(1-/2, )

proportion test
CI = ,

, CI =  ; , CI =  ; where , 其他就是差.

## Test

This section is a code test. Please ignore it and leave it alone. Thank you for your cooperation.

Template:Humor

## Test Reference

This section is where I'm testing the citation codes, to see if they are correctly written.

### Hooray!

1. Philip talked to Angela: Oh my God! This chink is an an extraordinary dumbfuck!
2. Andrew: Yeah! Get some pussies. You're the man, I appreciate that.
3. Philip: What the f- is wrong with you? What the f- is this? This is English? Are you f-ing retard?
4. Who told you that?
5. G. Orwell: 1984. Crimestop your thinkcrime! You just committed a facecrime!