Intereting Posts

QR factorization of a special structured matrix
Partial Derivatives on Manifolds – Is this conclusion right?
If $E/F$ is algebraic and every $f\in F$ has a root in $E$, why is $E$ algebraically closed?
Why does the volume of a hypersphere decrease in higher dimensions?
Closed Form for $~\int_0^1\frac{\text{arctanh }x}{\tan\left(\frac\pi2~x\right)}~dx$
Show that $A \setminus ( B \setminus C ) \equiv ( A \setminus B) \cup ( A \cap C )$
Prove that if $a^n\mid b^n$ then $a\mid b$
Show finite complement topology is, in fact, a topology
Polynomial irreducible – maximal ideal
Category Theory: homset preserves limits
Relationship between l'Hospital's rule and the least upper bound property.
Sum of two squares of an integer N, the simplest algorithm?
Why Doesn't This Series Converge?
Counting non-isomorphic relations
Proof of an alternative form of Fermat-Euler's theorem.

Suppose that I observe $k=4$ tanks with serial numbers $2,6,7,14$.

What is the best estimate for the total number of tanks $n$?

I assume the observations are drawn from a discrete uniform distribution with the interval $[1,n]$. I know that for a $[0,1]$ interval the expected maximum draw $m$ for $k$ draws is $1 – (1/(1+k))$. So I estimate $\frac {k}{k+1}$$(n-1)≈$ $m$, rearranged so $n≈$ $\frac {k+1

}{k}$$m+1$.

But the frequentist estimate from Wikipedia is defined as:

- maximum estimator method more known as MLE of a uniform distribution
- How to intuitively understand eigenvalue and eigenvector?
- Complete statistic: Poisson Distribution
- A conditional normal rv sequence, does the mean converges in probability
- Finding the number of red balls drawn before the first black ball is chosen
- If I flip a coin 1000 times in a row and it lands on heads all 1000 times, what is the probability that it's an unfair coin?

$n ≈ m-1 + $$\frac {m}{k}$

I suspect there is some flaw in the way I have extrapolated from one interval to another, but I would welcome an explanation of why I have gone wrong!

- What is the difference between all types of Markov Chains?
- Expected value and Variance
- Mode of lognormal distribution
- Deriving the mean of the Geometric Distribution
- Math Intuition and Natural Motivation Behind t-Student Distribution
- What is an intuitive meaning of $E(\overline { X } )$ and $Var(\overline { X } )$?
- Rating system incorporating experience
- Expression for $n$-th moment
- Likelihood Functon.
- In how many ways can 20 identical balls be distributed into 4 distinct boxes subject?

Just seen what went wrong. I accidentally put in a plus sign instead of a minus sign. Ugh:

$n≈$ $\frac {k+1}{k}$$m+1$ should be $n≈$ $\frac {k+1}{k}$$m-1$.

This is the same as the frequentist formula.

- How to evaluate $ \lim \limits_{n\to \infty} \sum \limits_ {k=1}^n \frac{k^n}{n^n}$?
- How can this integral expression for the difference between two $\zeta(s)$s be explained?
- Prove that every element $S \in SO(n)$ is a product of even numbers of reflections
- Sequences of sets property
- Polynomial: Is there a theorem that can save my proof when $K$ doesn't include $\mathbb C$
- Closed form for $\sum_{n=-\infty}^{\infty}\frac{1}{(n-a)^2+b^2}$.
- What is the principal cubic root of $-8$?
- Confusion about the hidden subgroup formulation of graph isomorphism
- Finding all solutions to a Diophantine equation involving partial sums of a given series
- If $n>m$, then the number of $m$-cycles in $S_n$ is given by $\frac{n(n-1)(n-2)\cdots(n-m+1)}{m}$.
- Transfinite Recursion Theorem
- Pairs of points exactly $1$ unit apart in the plane
- How do I prove that for every positive integer $n$, there exist $n$ consecutive positive integers, each of which is composite?
- Investigate the convergence of $\sum a_n$, where $a_n =\int_{0}^{1} \frac{x^n \sin(\pi x)}{1-x} dx$.
- Lefschetz number