The code created for this problem can be found here.

Problem 1

Let’s begin with a normal function:

\begin{equation} f(x) = (\sqrt{x}-1)^{2} \end{equation}

Taking just a normal Riemann sum, we see that, as expected, it converges to about \(0.167\) by the following values between bounds \([0,1]\) at different \(N\):

Problem 2

First, as we are implementing a discrete random walk, here’s a fun example; \(p=0.51\), \(\epsilon=0.001\).

Let \(X\) denote price and \(Y\) denote volatility. The two objects obey the following process:

\begin{equation} \begin{cases} \dd{X} = \mu X \dd{t} + XY \dd{W} \\ \dd{Y} = \sigma Y \dd{B} \end{cases} \end{equation}

where, \(W\) and \(B\) are correlated Brownian motions with correlation \(\rho\) — \(E[(\dd{W})(\dd{B})] = \rho \dd{t}\).

Let’s work with \(Y\) first. We understand that \(Y\) is some continuous variable \(e^{a}\). Therefore, \(\dv{Y}{t}=ae^{a}\). Therefore, \(dY = ae^{a}dt\). Finally, then \(\frac{\dd{Y}}{Y} = \frac{ae^{a}}{e^{a}}\dd{t} = a\).

The doctor-patient ratio in Haiti is 1 out of 67,000; a combination of malnutrition and malpractice results in a fatality rate of 47%.

In Breath, Eyes, Memory, the high rate of fatalities from birth is included as a part of a proverb in Sophie’s village. Ife tells that, of “three children” conceived by an old woman, “one dies in her body.” (Danticat 118)

Next Steps

Token: s_6285_15

Follow this link for the next step. You maybe able to continue to the next phrase of the game; it is also possible that you may have died during birth and would have to restart.

Apart from Russia, Central Africa and the Caribbeans have the highest average death rates of regions on Earth. Death is a pretty common occurrence, and—it appears—through the vicissitudes of the game you have died.

Better luck next time!

Despite having some access to education, actual success through it varies significantly as the resources are scarce. For instance, postsecondary education only shares 1% of educational spending in Martinique, so access to it is extremely limited.

In Black Shack Alley, José’s quarter scholarship—not enough to support his education—causes his mother to lament that they are “black, poor, and alone in the world” (Zobel 125): their station in Martinican society prevented their access to the already limited resource.