# Tagged Questions

For questions about estimation and how and when to estimate correctly

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### Estimation and combinatorics

I have a single user A, who needs to be matched to another user B. The criteria for matching A and B is 1 characteristic only. B is present in either one of the groups described below or present in ...
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### Bounding the absolute error of the linear approximation by $|E|\le\frac{n^2M}{2}\|\mathbf h\|^2$

Let $f: D\subseteq \Bbb R^n \to \Bbb R$ be a $C^2$ function. I'm trying to show that the absolute value of the error of the first order Taylor approximation of $f(\mathbf x+\mathbf h)$ is bounded ...
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### Proving OLS estimator of variance

According to Gujarati, author notes that in a simple linear equation form $Y_i=\alpha +\beta X_i + \epsilon_i$ where regression model is defined as $\hat Y_i =\hat \alpha + \hat \beta X_i$ OLS method ...
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### expectation and variance of an implicit estimator

Suppose the following equation holds \begin{align*} p_2=\int\limits_{-\infty}^{\Phi^{-1}(p)}\int\limits_{-\infty}^{\Phi^{-1}(p)} \frac{1}{2\pi\sqrt{1-\rho^2}}\exp\bigg({-\frac{1}{2}\frac{x^2-\rho xy+...
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### Expectation and Variance of an Estimator

Imagene following equation holds \begin{align*} p_2=\int\limits_{-\infty}^{\Phi^{-1}(p)}\int\limits_{-\infty}^{\Phi^{-1}(p)} \frac{1}{2\pi\sqrt{1-\rho^2}}\exp\bigg({-\frac{1}{2}\frac{x^2-\rho xy+y^2}{...
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### Show that an estimator is unbiased and it's variance goes towards 0? Poisson distribution

Let X be Poisson Distributed with expectation λt. Show that the estimator is unbiased and has a variance that goes towards 0 when the times goes to infinity. λ^=X/t I know that for these questions ...
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### Knowing the rates of gain and loss, estimate the average amount.

This question was presented to me as such: Say that people grow 100 hairs a day and lose 100 hairs a day and hairs have a lifespan of 100 days. Estimate how much hair an average person would have. ...
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### How to know when to use t-value or z-value?

I'm doing 2 statistics exercises: The 1st: An electrical firm manufactures light bulbs that have a length of life that is approximately normally distributed with a standard deviation of 40 hours. If ...
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### Asymptotic lower bound of this function

Suppose that $n$ is an even number. Let $$f(n)=\frac{\sum_{j=1}^{n/2}\binom{n}{2j}\log(2j)}{2^{n-1}}.$$ Can we find some function $g(n)$ (e.g. $\log(n)$ or $n^\alpha$) such that $f(n)=\Omega(g(n))$? ...
### unbounded variation of $\sin(x)/x$
How can I show that the variation of $sin(x)/x$ is unbounded? Could you please help me. I know that I have to use but how can I rough estimate that this is bigger than infinity?