# Tagged Questions

For questions about estimation and how and when to estimate correctly

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### Understanding the steps taken in a calculation of the maximum profile likelihood of a simple ODE, given some data

I'm trying to understand a calculation made in a paper (section 2 from the supplementary contents of ...
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### Cramer-Blackwell estimator for uniform distribution.

I've got two estimators of parameter $\alpha$ in the distribution $X=X_1,...,X_n$, where $X_i$s are i.i.d. uniform random variables on the interval of $(0,\alpha)$. These two estimators are: ...
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### Estimating confidence Interval for unknown Variance, Normal distribution

I've been stuck with this question for a while: I've learnt how to use t-distribution to estimate CIs for an unknown variance, but I'm unsure how that applies to this situation. Any help would be ...
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### How can I calculate missing values from a table listing of areas and prices? [on hold]

I have a set of objects of different sizes (measured in square metres). I know the price of some of them. I want to use the known prices to find the missing prices. Here is the data I have: ...
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### Probability of island having 8 people born with disease, estimate?

The chances of being born with a certain disease are estimated as $1$ in $1200$. What is a good estimate of the chance that an island with $10000$ inhabitants has precisely $8$ people born with that ...
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### Supremum of $\cot(\pi z)$ where $z$ is on circle with radius $n+1/2$

I try to estimate the supremum of $|\cot(\pi z)|$ and where $z=(n+1/2) e^{i t}$, $n\in\mathbb N$ and $t\in[0,2\pi)$. I should be a constant. So far I did by wiriting it in exponential form and ...
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### Fitting a model to a collection of binomial proportions, based on varying (large) sample sizes.

I have a multi-parameter bivariate function, say $f(i,j)$ that I want to use to predict the entries of a matrix $M(i,j)$, the entries of which are binomial probabilities based on varying sample sizes, ...
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### Maximum Likelihood Estimation with 2 parameters for a Poisson distribution

I have two observations from a Poisson distribution. The first one ($N_r$) come with a Poisson distribution with mean $k_1$. For the second one ($N_e$) I know that $N_e - M$ also come from the same ...
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### Lower bound of KL-divergence between unknown and known distribution

Suppose I have two multivariate continuous random variables $X$ and $\hat{X}$ with underlying probability distributions $P_{X}$ and $P_{\hat{X}}$, where $P_{\hat{X}}$ is a Gaussian approximation of ...
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### Estimation, Upper limits, Lower limits

Two rods of length 2.6 cm and 3.5 cm are measured correct to the nearest 0.2 cm. The two rod are joined together, find the lower and upper limit of the new rod. I get stuck. HOw to do?
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I'm now extreamly tierd of not pulling off this equation. $$\sum_{i=1}^n (y_i-\alpha)^2= \frac{2n\sum_{i=1}^n (y_i - \alpha)}{\sum_{i=1}^n (\frac{1}{y_i - \alpha})}$$ Solve for $\alpha$, y is a ...
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I’m stuck on the following problem. There are two sources $S_A$ and $S_B$ at the ends of a channel. Both are made up of a white noise component $W_i$ plus an impulsive component $I_i$: $S_A = W_A + ... 1answer 13 views ### derivation of$\theta(x)=\int_{a}^{x}\varphi (y)dy - (\int_{a}^{b}\varphi(y)dy)\psi(x)$and °L^2$-norm estimation

Let $I=(a,b)$, $u\in L^2(I)$ and $\psi\in C^{\infty}(I)$ such that $\psi=0$ on $(a,a+\epsilon)$ and $\psi=1$ on $(b-\epsilon , b)$ for sufficient small $\epsilon$. Let $\varphi\in C_C^\infty (I)$ and ...
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### Estimate parameters of a quadratic function

Suppose that we have two data points which tell us about the output of some function $f(x)$: $(0, 50)$ $(10, 150)$ We know that the function is quadratic (so it's something like $ax^2 + bx + c$). ...
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### Saturating space so that at least two lines are close enough

All lines in what follows pass through the origin. The only reason for the angle $2\pi/3$ below is that this is how I began wondering about these questions. Picture the unit disc $S^2$, by which I ...
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### Why integral is equal to zero

I wonder why under assumption that w>>$\frac{1}{T}$ then $\int_{0}^{T} sin(wt)dt$ is approximately zero? Since the integral should be like- $\frac{cos(wt)}{w}$ from $0$ to $T$ and after plugging the ...
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### How to estimate numbers like $(19/20)^{30}$

Is it possible to estimate by hand what is the value of expresion like $(19/20)^{30}$? $$19/20 = 0.95$$ but $$(19/20)^{30} \approx 0.2146$$ So it is totally different number.
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