# Tagged Questions

0answers
79 views

### pricing of heat rate-linked derivative [migrated]

It's a simplified model. Suppose $U_t$ is a random variables subject to Lognormal($x_1$, $z_1^2$)distribution. $V_t$ is a random variables subject to Lognormal($x_2$, $z_2^2$)distribution. Suppose ...
1answer
32 views

### Optimize winnings in a money making game.

So, given a continuous random variable A (with some density and CDF function), and a value I choose V, what is the equation to determine the best value V to maximize my earnings given that I will be ...
2answers
35 views

### gradient descent optimal step size

Suppose a differentiable, convex function $F(x)$ exists. Then $b = a - \gamma\bigtriangledown F(a)$ imples that $F(b) <= F(a)$ given $\gamma$ is chosen properly. The goal is to find the optimal ...
1answer
47 views

### Optimal strategy puzzle

Play a game with an urn. $75$ blue balls. $25$ red balls. $1$ yellow ball. you get a dollar for every red and if you select the yellow you lose everything. what should be your strategy in the game. ...
0answers
31 views

### Facets of the convex hull as solution of an optimization problem?

Given $N$ points $x_1, x_2, ..., x_N \in \mathbb{R}^n$, consider their convex hull \mathcal{C} = \text{conv}( \{ x_1, ..., x_n \} ) = \bigcap_{j=1}^{J} \{ x \in \mathbb{R}^n : \ A_j x \leq b_j \} ...
1answer
22 views

### What is the optimal stopping point for an experiment when expecting unknown event

Assume we notice that stock prices are rising and we can deduce we are in a bubble. Assume we start at $w(0)=0$ worth at time $t=0$ and the value grows linearly with time $(w(t)=t)$. We know that ...
2answers
61 views

### Anyone saw this interesting function before?

Say $\theta\in\Re^n$ and $\theta_i\in(0,1)$ for all $i$. Define $$f(\theta) = \frac{1}{n}\sum_i^n\{(1-\theta_i)\log(1-\theta_i)+\theta_i\log\theta_i\}$$ It is easy to see the minimizer of ...
3answers
50 views

### Packing radios into cartons - why is my solution wrong?

A manufacturer of car radios ships them to retailers in cartons of $n$ radios. The profit per radio is $\$59.50$, minus shipping cost of$\$25$ per carton, so the profit is $59.5n-25$ dollars per ...
1answer
77 views

### Inverse transform sampling

I know the basic idea is to generate a random number from $U(0,1)$, find the inverse cumulative distribution function $F^{-1}$ and then take $x = F^{-1}(U)$. If you were plot a histogram of say 1000 ...
1answer
140 views

### Optimal Yahtzee (Dice roll) decisions: Probability and weighting choices

I'm a senior in computer science, and I have a hobby of taking on little projects that I find interesting. My current one is a Yahtzee optimal play solver. One would enter their current roll, and it ...
0answers
31 views

### Optimal distribution with moment conditions

Basically, I want to find a probability distribution which maximizes a convex objective function and satisfies two moment constraints. For given $\bar x$, $m_{n-1}$, $m_n$  \max_{f(x)} ...
1answer
135 views

### Need help with proof for arbitrage betting

Recently I came across this article about sports betting arbitrage: http://www.sportsbettingworm.com/arbitrage-calculations/index.html. The article gives formulas for calculating arbitrage profit and ...
1answer
48 views

### Optimizing a physician's medical test plan

I have come across the following optimization problem: "A patient presents himself with symptoms to a physician. The physician has a set of $n$ medical tests, where each test $i$ has costs $c_i$ ...
1answer
14 views

1answer
74 views

### what math topic is this kind of example part of? or what is needed to understand how to solve it? [closed]

we 100000000 sets/locations. each set has, A = % chance of finding a cure (there are many different types of cures) for cancer B = time it takes to extract a cure to caner C = the optimal % chance (IN ...
0answers
88 views

### Differential Equations, Probability/Statistics, Optimization Problem - Relations?

While I am working on some physical/mathematical problems, I feel strongly that these three areas are almost the identical thing, except that they have different methods/from different aspects to ...
1answer
116 views

### Secretary problem for unknown n?

So one of my good friends is starting to date again (after being out of the country for two years), and I think that it might be helpful, or at least fun, to keep track of her dates in a ranked ...
0answers
37 views

### How to go about optimizing this function? (Maximizing)

If we are given a fixed integer $N > 0$ of choices we can pick out of a pool of $k$ values $c_0, \cdots, c_k$ (with repetitions allowed and $c_i > 0 \forall i$) and we want to maximize the ...
2answers
37 views

### Maximizing the time we reach to a threshold in a series of numbers

I have a problem and I really don't know what kind of mathematical method should I apply to solve or model my problem. I would be thankful If anyone can give me some answer or help. Suppose we have ...
1answer
38 views

### Uniform Continuous R.V. - Optimization

working on this problem: A road construction company needs to decide where to place an emergency phone on a stretch of road of length L. Suppose that accidents can happen uniformly at random ...
0answers
78 views

### Select positions for strongest defense given probability(position, target) scores. [closed]

In a game of tower defense, I want to place archers to optimize survival time. I have ~10 towers, and I am allowed one archer per tower. The towers have 50 to 300 vantage points each. Once an archer ...
2answers
512 views

### One vs multiple servers - problem

Consider the following problem: We have a simple queueing system with $\lambda%$ - probabilistic intensity of queries per some predefined time interval. Now, we can arrange the system as a single ...
1answer
104 views

### Strategy to maximize no. of balls from N boxes

If you have N boxes each containing distinct number of balls and you are allowed to choose at most ...
2answers
389 views

### Grad degree that mainly deals with probability/game theory/optimization?

I'm currently working but am going to take classes as a non-degree student to beef up the math part of my background. I've only taken calc 1-3, ODEs, linear algebra, logic, and decision theory so my ...
2answers
79 views

### is there a solution to the following maximization problem such that $a = b$?

Let $X = (X_1,...,X_n)$ be a vector of $n$ random variables. Consider the following maximization problem: $\max\limits_{a,b} \;\mathrm{Cov}(a\cdot X, b \cdot X)$ under the constraint that \$\|a\|_2 = ...
1answer
63 views

### Derivatives with respect to a symmetric matrix, with an application to maximum likelihood

I am quite unsure about this whole matter of differentiation with respect to a matrix. First, I'd like a good (online hopefully) reference for getting up to speed on the theory - as opposed to a bunch ...
4answers
103 views

### Optimizing the expectancy

The following problem is about optimization. It is not a homework, but rather a natural question to ask to oneself afterwards. Here it is. Consider a road of length $L$ between two cities $A$ and ...
1answer
179 views

### Stochastic assignment problem

Given an $n \times n$ real matrix $C$, we can try to maximize $$\Phi(C, \pi) = \frac{1}{n} \sum_{i} C_{i,\pi(i)}$$ over $\pi \in S_n$, the set of all permutations on $n$ objects. What can one say ...
1answer
295 views

### Manifold with minimum surface distance between two points

The book "The World is Flat" uses flatness as a metaphor for a global economy. In fact, a spherical world would seem to be better than a flat world in terms of reducing the distances between two ...
2answers
323 views

### Generalization of the Sultan's dowry problem

We know the solution of the Sultan's dowry problem: To reject the first $n/e$ candidates and then to select the first who exceeds the best of the sample. How to find the best strategy if we want ...
1answer
164 views

### Maximize normal density function over a subset

For a 2D Normal distribution $N(0, \left[ \begin{array}{cc} 1 & -1/4 \\ -1/4 & 1 \end{array} \right])$, I am now trying to maximize its density function over $\{ x\geq 10, y \geq 10 \}$. My ...
3answers
411 views

### Optimally combining samples to estimate averages

Suppose I have two tables, each of unknown size, and I'd like to estimate the average of their true sizes. I hire 2 contractors: one guarantees good precision (i.e., her measurement ...
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