The Science of Life

As promised last time , I will cover examples of discrete and continuous probability distributions. Top: Discrete Probability Middle: Continuous Probability Bottom: Disjointed Probability Disjointed won't be covered in this course. Discrete Probability Model (example): The following table represents the probabilities of people of certain age groups living alone, living with a spouse, or living with at least one person who is not a spouse. 15-19 20-24 25-34 35-44 Alone 0.001 0.011 0.031 0.030 With Spouse 0.001 0.023 0.155 0.216 With others 0.169 0.132 0.142 0.089 Because there is a finite amount of categories which has a non-zero probability of occurring, this is considered to be a discrete probability model.  Then again, I am assuming that it is a probability model.  Remember from the first lecture th...

Probability is the foundation of everything we do in Statistics.  There are two types of probability: discrete and continuous.  Discrete probability is when there are distinct probabilities for different values (represented by bars), while continuous probability is where the probabilities change smoothly with the value (represented by a smooth curve).  This is better described by images.  These are two types of probability models and are therefor treated different. Discrete Probabilities of Dice Rolls. Continuous Probability Distribution of Pounds of Waste Produced. We have what is called Probability Models.  Probability models have a sample space (denoted by an S).  Probabilities are assigned to sample points in sample space.  For the continuous Standard Normal Distribution, the x axis is the sample point and the y axis (denoted P(E)) is the probability axis.  In the graphs above, the values we want to get a probability for is on th...

I am currently working on a YouTube project called "The Science They Don't Want You to Know", where I will cover science that various organizations and individuals don't want to be known by the general population for one reason or another.  It will be set up in seasons, since there are so many related topics to consider. The first season will cover conspiracy theories which affect public health.  In it, I will run be dependent on two papers, one which revolves around the mathematics of known conspiracies, and the other which describes the psychology of conspiracy theorists.  The math paper , which is written by Professor David Grimes of the University of Oxford, looks at various conspiracies which have been leaked to the public.  Examples of this include the NSA spying on us , the old syphilis "experiments" , and Watergate.  What he did was to use these known cases of conspiracies to develop a model for figuring out what the probability would be fo...

I will begin with a conclusion which is... uncomfortable to say the least.  Then I will walk through how this conclusion was reached.  It is something which will have you call bullshit on me off the bat, but please hear me out (or read me out?).  I have written a theoretical ecology paper last summer which shows that the human population will stop growing no later than 2031, and will drop (not plateau) shortly thereafter.  The cause?  Resource depletion.  Please, read me out. Now, how did I come to this conclusion?  By the power of maths! In ecology, there is a situation where, when a major cause of death for a species is removed, the population of that species goes through what is called exponential growth .  This is where the rate of change (percent change) is constant, and since the population today is more than it was yesterday, the greater the net change.  Let's say the percent change is 1% and we started with $100.  Tomor...

In every physical science, we rely heavily on mathematical models to accomplish further scientific research.  (Yes, even you biologists and organic chemists; you just have the mathematical models hidden.)  Mathematical models are the key to all scientific research.  (And for those reading this from outside of the United States, I will use the word "sciences" in place of the term "physical sciences" from here on out; be prepared for that.) This brings up a key question; what exactly is a mathematical model? It would be good to have an equation fall under a mathematical model.  This can be the case, but more often than not, one equation is insufficient.  It also doesn't have to contain equations; there can also be inequalities, where a value is either less than or greater than a certain quantity. Mathematical models are descriptions of a system with mathematical language , which can be one or many equations or inequalities.  This is more of a...

I apologize for a longer-than-acceptable absence. My academic progress is getting in the way of so much of my life right now, including but not limited to this blog. I will, however, persevere in continuing with it – both the academics as well as the blog. I have also been working on a few projects outside of academia and outside of this blog. This includes a new website which incorporates poetry, chemistry, undergraduate papers, ACS news, and my tutoring in chemistry. For those of you curious, it can be found at http://poetchem.alexandersdesigns.net/ .  Over the course of the next few months, I will be transitioning this blog over there. For this blog entry, I will detail how one of my classes – in particular, Calculus III – relates to the real world. This is one project I have been working on for the past few semesters.  This will also be my final extra credit project for that course. There is something you have to understand about the realm of mathematics,...