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If it is $50p$ for every half mile then the formula is (included max to avoid the use of "if") $$f(x,y)=3+\frac{\lfloor\max\{2x-4,0\}\rfloor}{2}\cdot 0.50+0.50\cdot y.$$ Note that this answer is adapted to the change included in your comment and doesn't fit with the original table of prizes.

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To round a number $z$ to the nearest multiple of $a$, you can use $\lfloor \frac za+\frac12\rfloor \cdot a$. Hence you can use $$f(x,y)=\begin{cases}3+0.50y&\text{if x\le 2}\\ .50\cdot \bigl(\lfloor 2x+\frac12\rfloor +y+2\bigr)&\text{if x>2}\end{cases}$$

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You can evaluate everything in capital letters to make your expression $a^{2k-1}b+c$ As all the capital letters are positive, we have $c \gt 0$ If $a,b$ have the same sign, you are sunk as the first term will be positive, too. As we have $b=Wa-stuff$, we assume $a \gt 0, b \lt 0$ So we have to assume $AW \gt X$. Then $b \lt 0$ will be satisfied. Note ...

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It is possible to solve analytically the system of three ODEs. This could be useful for numerical applications, in order to obtain more accurate numerical results than with the the usual methods of numerical solving of the ODEs. The solution is presented on a parametric form : For given $R$, compute the corresponding $S , I, t$ with the formulas. This is ...

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Mathematics is agnostic to units. Mathematical models, however, do care very much about units. (The numeral 1 attached to the units 'seconds' and 'hour' give two very different meanings.) So it is extremely important that when you do write down a model and do actual analysis and computations on it, you include conversion factors which makes your unit ...

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Yes, this is described by exponential distribution http://en.wikipedia.org/wiki/Exponential_distribution. Briefly, if $\lambda$ the mean of your Poisson distribution, namely the averaged number of ships per day, then $1/\lambda$ is the averaged time ( in day units) between ships.. Very natural.

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In a complete market the absence of arbitrage implies the existence of an equivalent probability measure under which asset prices are martingales. The fair value of a derivative security that can be replicated with a dynamic hedging strategy can then be determined as an expected value under this measure. Proving this in a continuous-time stochastic ...

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Given an urn containing $n$ labeled balls, let $p_k$ be the probability that $k$ balls chosen at random (with replacement) contains a repeated ball. The Birthday Paradox says that, when $n=365$, we have $p_k>0.5$ whenever $k \geq 23$ (the "paradox" is that $23$ seems surprisingly low). The Birthday Paradox is often phrased in terms of birthdays since it ...

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Do you mean the fact that if you select 23 people at random, there is a 50% probability that at least one pair of these people will die on the same day of the year (under the usual assumptions of only 365 days in the year and equal probability of dying on any given day). Aside from being a bit morbid, if you select your random sample from among the living ...

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It's ok to do mathematically, just keep in mind that it means completely ignoring $X_4$ when "the blinds are closed".

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Another alternative approach to this (if you don't want to confuse yourself with long equations or if you need to do it quickly on your mobile calculator ....etc): 1) you get the ratio between probability of losing to winning 2) then multiply that ratio by the Percentage of bid amount forfeited for losing. 3) Then You can simply multiply the result by "V" ...

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