# Tagged Questions

For questions about estimation and how and when to estimate correctly

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### How many bathtubs in a min?

During the summer about $750,000$ gallons of water fall over the edge of Niagara Falls every second. If an Olympic sized swimming pool holds about $660,000$ gallons of water, how many Olympic sized ...
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### Estimating the Average and Standard Deviation of a Population based on a Sample with Missing Data with Known Ranks

I need a way to shows me how the parameters of PDF, log-normal in this case, can be estimated based on a set with missing data points at the tail end of a sample. For example, Consider we had 20 ...
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### How to estimate magnitude of expontent?

When given an exponent, such as 6^12, is there a simple way to approximate how large(magnitude) the result is, without performing the calculation? Is this method accurate for large exponents?
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### Confidence Interval for Incidence Rates

I have a huge sample of patients followed up for a certain Event. I would like to calculate the following crude incident rates: #{Events}/(1000*PersonYear). My sample is big enough to assume that this ...
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### Solve the system of equations by variable estimation

Solve the system of equations: $\left\{\begin{array}{l}(x-1)\sqrt{x-y^2}=y(x-2y+1)\\y\sqrt{x-1}+3\sqrt{x-y^2}=2x+y-1\end{array}\right.$ I guess there is only one solution $(x;y)=(2;1)$. This is my ...
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### Estimate how many times to flip a coin to get at least 30 heads with probability of 80%

Im completely stumped by this problem. It goes as follows: Estimate how many times a fair coin must be thrown in order to obtain at least 30 heads with a probability of 0.80. Ive tried playing with ...
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### Berry-Esseen bound for binomial distribution

From the Berry-Essen theorem I can deduce $$\sup_{x\in\mathbb R}\left|P\left(\frac{B(p,n)-np}{\sqrt{npq}} \le x\right) - \Phi(x)\right| \le \frac{C(p^2+q^2)}{\sqrt{npq}}$$ with $C \le 0.4748$. My ...
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### Bayes estimator under squared error loss

Consider one random variable X from the Bernoulli distribution with parameter θ. Let p, the prior density, be equal to 6θ(1 − θ), for θ ∈ (0, 1). Under squared error loss, L(t, θ) = (t − θ)$^2$, the ...
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### Can I adjust linear growth of a a subpopulation to a linear decay of the general population?

I need to estimate the amount of CF patients in Poland in the next four years. I have: estimations of the Polish population for the future years a CF patients' register for the last couple of years ...
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### What are the bounds (upper and lower) for $|A+A|$?

Let $A$ be a finite set of real (or complex) numbers. If I consider sets with small sizes, we have that: If $A$ is the empty set, then $A+A$ is also empty. If $A$ is a singleton, then $A+A$ is ...
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### Sampling with no duplicates

I am sampling a population of unknown size and unknown distribution. The sample will be taken over distinct time intervals, but I have to reject any duplicates in the given time interval. The sample ...
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### Polynomial roots finding algorithm

My initial problem is a parameter estimation problem that is solved by minimining a least-square criterion with the Gauss-Newton algorithm. However finding a good initial iterate is very tedious. I'...
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### Estimating compound growth

I have a compound interest function with the following parameters: Value at time 0 = 13.8 Interest rate = 0.05 time interval = 10 I need to check quickly, (without a calculator, only pen and paper) ...
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### Estimating the size of my population

I have a following problem: Imagine you have a hat with many different balls in it and you want to estimate, how many balls are totally in the hat. The only think you are allowed to do is to take one ...
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