# User contributions

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- 14:48, 14 July 2019
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**(+854)** . . N Definition:Sufficient Statistic (Created page with "== Definition == <onlyinclude> Let $X_1, X_2, \ldots, X_n$ form a random sample from a population indexed by a Definit...") (current) - 12:55, 13 July 2019 (diff | hist) . . (+181) . . Definition:Convergence in Probability (current)
- 12:49, 13 July 2019
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**(+702)** . . N Strong Law of Large Numbers (Created page with "== Theorem == <onlyinclude> Let $P$ be a population. Let $P$ have mean $\mu$ and finite variance....") (current) - 12:46, 13 July 2019 (diff | hist) . . (0) . . Definition:Almost Sure Convergence (current)
- 12:46, 13 July 2019 (diff | hist) . . (+8) . . Definition:Almost Sure Convergence (more general)
- 12:44, 13 July 2019 (diff | hist) . . (-32) . . Definition:Almost Sure Convergence
- 12:44, 13 July 2019
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**(+771)** . . N Definition:Almost Sure Convergence (Created page with "== Definition == <onlyinclude> Let $\sequence {X_n}_{n \ge 1}$ be a sequence of random variables. Let $b$ be a Defini...") - 09:36, 13 July 2019 (diff | hist) . . (+8) . . Definition:Random Sample (so it applies for discrete variables too) (current)
- 09:32, 13 July 2019 (diff | hist) . . (-21) . . Variance of Sample Mean (current)
- 09:31, 13 July 2019 (diff | hist) . . (-1) . . Definition:Random Sample
- 09:31, 13 July 2019 (diff | hist) . . (+7) . . Weak Law of Large Numbers (current)
- 09:30, 13 July 2019 (diff | hist) . . (-22) . . Mean of Random Sample from Chi-Squared Distribution has Gamma Distribution (current)
- 09:30, 13 July 2019 (diff | hist) . . (-22) . . Variance of Random Sample from Gaussian Distribution has Chi-Squared Distribution (current)
- 09:29, 13 July 2019 (diff | hist) . . (-21) . . Sample Mean is Unbiased Estimator of Population Mean (current)
- 09:29, 13 July 2019 (diff | hist) . . (-21) . . Bessel's Correction (current)
- 09:29, 13 July 2019 (diff | hist) . . (-21) . . Bias of Sample Variance (current)
- 09:28, 13 July 2019
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**(+943)** . . N Definition:Random Sample (Created page with "== Definition == <onlyinclude> Let $X_i$ be a random variable with $\Img {X_i} = \Omega$, for all $1 \le i \le n$. Let $f_i$ be the Definitio...") - 13:54, 11 July 2019 (diff | hist) . . (-175) . . Bias of Sample Variance
- 13:51, 11 July 2019 (diff | hist) . . (+8) . . Variance of Sample Mean
- 13:50, 11 July 2019
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**(+974)** . . N Variance of Sample Mean (Created page with "== Theorem == <onlyinclude> Let $X_1, X_2, \ldots, X_n$ be random samples from a population with Definition:Expectation|...") - 10:06, 11 July 2019 (diff | hist) . . (-1) . . Definition:Convergence in Probability
- 10:05, 11 July 2019 (diff | hist) . . (-1) . . Weak Law of Large Numbers
- 08:24, 11 July 2019
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**(+821)** . . N Definition:Convergence in Distribution (Created page with "== Definition == <onlyinclude> Let $\sequence {X_n}_{n \ge 1}$ be an sequence of random variables. Let $X$ be a Defin...") - 05:55, 11 July 2019
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**(+860)** . . N Variance of Linear Combination of Random Variables/Corollary (Created page with "== Theorem == <onlyinclude> Let $X$ and $Y$ be independent random variables. </onlyinclude> Let the Definition:Variance|varianc...") (current) - 05:50, 11 July 2019 (diff | hist) . . (+150) . . Variance of Linear Combination of Random Variables (current)
- 05:47, 11 July 2019 (diff | hist) . . (-2) . . Sample Mean is Unbiased Estimator of Population Mean
- 05:47, 11 July 2019 (diff | hist) . . (-2) . . Bessel's Correction
- 05:46, 11 July 2019 (diff | hist) . . (-2) . . Bias of Sample Variance
- 05:39, 11 July 2019
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**(+2,304)** . . N Weak Law of Large Numbers (Created page with "== Theorem == <onlyinclude> Let $P$ be a population. Let $P$ have mean $\mu$ and finite variance....") - 19:50, 10 July 2019 (diff | hist) . . (0) . . Definition:Convergence in Probability
- 19:50, 10 July 2019 (diff | hist) . . (+15) . . Definition:Convergence in Probability
- 19:50, 10 July 2019
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**(+717)** . . N Definition:Convergence in Probability (Created page with "== Definition == <onlyinclude> Let $\sequence {X_n}_{n \ge 1}$ be an sequence of random variables. Let $b$ be a Defin...") - 19:05, 10 July 2019 (diff | hist) . . (+31) . . N Category:Chebyshev's Inequality (Created page with "Category:Probability Theory") (current)
- 19:05, 10 July 2019 (diff | hist) . . (+28) . . Chebyshev's Inequality/Proof 2 (current)
- 19:04, 10 July 2019
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**(-555)** . . Chebyshev's Inequality (current) - 19:04, 10 July 2019
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**(+894)** . . N Chebyshev's Inequality/Proof 1 (Created page with "== Theorem == {{:Chebyshev's Inequality}} == Proof == <onlyinclude> Let $f$ be the function: :$\map f x = \begin{cases} k^2\sigma^2 & : \size {x - \mu} \ge k\sigma \\ 0 & :...") (current) - 18:59, 10 July 2019
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**(+577)** . . N Chebyshev's Inequality/Proof 2 (Created page with "== Theorem == {{:Chebyshev's Inequality}} == Proof == Note that as $k > 0$ and $\sigma > 0$, we have $k \sigma > 0$. We therefore have: {{begin-eqn}} {{eqn | l = \map \Pr...") - 07:40, 9 July 2019
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**(+679)** . . N Probability Density Function of Convolution of Probability Distributions (Created page with "== Theorem == <onlyinclude> Let $X$ and $Y$ be continuous independent random variables....") (current) - 07:28, 9 July 2019 (diff | hist) . . (0) . . m Definition:Convolution of Probability Distributions (Caliburn moved page Definition:Convolution (Probability Theory) to Definition:Convolution of Probability Distributions without leaving a redirect: this seems to be more consistent) (current)
- 07:25, 9 July 2019 (diff | hist) . . (-1) . . Definition:Convolution of Probability Distributions
- 07:25, 9 July 2019
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**(+583)** . . N Definition:Convolution of Probability Distributions (Created page with "== Definition == <onlyinclude> Let $X$ and $Y$ be independent random variables. Let $Z = X + Y$. The Definition:Probability...") - 07:01, 9 July 2019 (diff | hist) . . (+4) . . User:Caliburn/todo (current)
- 06:39, 9 July 2019 (diff | hist) . . (+122) . . Second Order ODE/y'' - y' - 6 y = exp -x (current)
- 06:37, 9 July 2019
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**(+3,369)** . . N Second Order ODE/y'' - y' - 6 y = exp -x/Proof 3 (Created page with "== Theorem == {{:Second Order ODE/y'' - y' - 6 y = exp -x}} == Proof == <onlyinclude> Taking Laplace transforms: :$\laptrans {y'' - y' - 6...") (current) - 05:46, 9 July 2019 (diff | hist) . . (0) . . Second Order ODE/y'' + 4 y = 8 x^2 - 4 x/Proof 2 (typo) (current)
- 15:45, 8 July 2019 (diff | hist) . . (+54) . . Second Order ODE/y'' + 4 y = 8 x^2 - 4 x (current)
- 15:45, 8 July 2019 (diff | hist) . . (+41) . . N Category:Second Order ODE/y'' + 4 y = 8 x^2 - 4 x (Created page with "Category:Examples of Second Order ODE") (current)
- 15:45, 8 July 2019
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**(-1,800)** . . Second Order ODE/y'' + 4 y = 8 x^2 - 4 x - 15:44, 8 July 2019 (diff | hist) . . (+54) . . Second Order ODE/y'' + 4 y = 8 x^2 - 4 x/Proof 1
- 15:44, 8 July 2019
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**(+2,132)** . . N Second Order ODE/y'' + 4 y = 8 x^2 - 4 x/Proof 1 (Created page with "== Theorem == {{:Second Order ODE/y'' + 4 y = 8 x^2 - 4 x}} == Proof == <onlyinclude> It can be seen that $(1)$ is a Definition:Nonhomogeneous Linear Second Order ODE|nonho...")

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