In this week we will be learning about random variables and many more things…
Monday: Feb 14, 2021
Random variables come in many forms, sometimes 1 dimensional, 2 dimensional, and other times causally related to themselves!
It can be interesting studying them and we hope to share this same idea as the course goes on. First, rather than formally defining a random variable, we’ll just give the informal verbal description.
Description: A random variable is like a number with a fixed domain that has entropy (variation) modeled by a probability distribution. We write a random variable with capital letters, so $X$ as written is a random variable. The distribution is noted using a $\sim$ symbol. All random variables follow some distribution! And we can write the relation as $X \sim D$ where $D$ is the distribution. Colloquially, a die in casino games is like a random variable, it varies what the roll is and does it with a uniform probability distribution (assuming the die is fair).
all hypothetical…
In the class, we’ll be coding a lot, using python. Just to familiarize you guys right now, some example python code is given below:
print("it's python!") #prints a basic string to the consoleWe’ll also be doing basic newtonian physics concerning velocities, and integrals, you need to know the basic work integral for vectors:
\[W = \int \vec{F} \cdot d\vec{x}\]and a little bit of chemistry as well, take the ion for sodium $\text{Na}^+$ as well as the electrolysis equation:
\[2H_2O \to 2H_2 + O_2\](and so on, just showing how writing math, stats, and even physics/chemistry notes for the week can be easy in a .md interface).