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Introduction edit
 | This page is still under construction. Therefore some parts of it don't make any senses. Please don't laugh your ass off. |
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 edit
User:Disavian/Userboxes/Ubx-Night
Chapter 2 edit
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 edit
: from n choose (组合) k; : from n permute (排列) k.
- intersection, : union, Ac: complementary. ; factorials (n!);
Chapter 4 edit
- 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？].
近似: When it’s large (n≥30) and σ is known, we can use z-CI instead: = ,
where = invNorm(1-/2), 1-/2 = (1-CC)/2. [ = 1.645; = 1.960; = 2.576]
已知置信区间，求最小样本容量: for z-CI, , therefore . Why not t-CI ( )? Because n-1 in you cannot bring it out.
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 edit
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).
近似: z-test: when σ is known and sample size is very large (n>30).
- 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 edit
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 edit
| | This section is a code test. Please ignore it and leave it alone. Thank you for your cooperation. |
 | This page contains material that is kept because it is considered humorous. Such material is not meant to be taken seriously. |
 | This article is written by a dumbfuck and may require cleanup. Please help improve it by rewriting it in an non-dumbfucking style. |
Laugh My Ass Off edit
The person is out of his mind. User:Fastily/Userboxes/Hopelesseditingaddict User:Strdst grl/ubx/mandelbrot User:Teinesavaii/Polynesian Userboxes/Shrink User:UBX/For rent User:Strdst grl/ubx/bouncing User:Edit Centric/UBX/ArmBears User:P.B. Pilhet/UBX/NDC
Major edit
Minor edit
Test Reference edit
This section is where I'm testing the citation codes, to see if they are correctly written.
Hooray! edit
- ↑ Philip talked to Angela: Oh my God! This chink is an an extraordinary dumbfuck!
- ↑ Andrew: Yeah! Get some pussies. You're the man, I appreciate that.
- ↑ Philip: What the f- is wrong with you? What the f- is this? This is English? Are you f-ing retard?
- ↑ Who told you that?
- ↑ G. Orwell: 1984. Crimestop your thinkcrime! You just committed a facecrime!