<p>Both correlation and covariance are an indicator of the relationship between two variables. They indicate whether the variables are positively or negatively related.</p>



<p>The correlation also indicates the degree to which the two variables are related. It's a translation of covariance into a unit-less measure that we can understand (-1.0 to 1.0). The correlation of the variable with itself is always 1.</p>



<p>This video takes an example to explain the two concepts:</p>



<figure><iframe width="560" height="315" src="https://www.youtube.com/embed/35NWFr53cgA" allowfullscreen=""></iframe></figure>



<p>This video is developed by David from Bionic Turtle.</p>

Correlation and Covariance

When drawing an inference (from a sample statistic, about a population parameter), there can be two types of errors: Type I and Type II.

Type I error, also known as error of the first kind, occurs when the null hypothesis is true, but is rejected.

Type II error, also known as the error of the second kind, occurs when the null hypothesis is false, but is accepted as true.

The following video explains these errors with examples.



This video is developed by David from Bionic Turtle.

Type I and Type II Errors

<p>This video is a short primer on the concepts of permutations and combinations.</p>



<p>Both permutations and combinations count the ways that (r) objects can be taken from a group of (n) objects, but permutations are arrangements (sequence matters), while combinations are selections (order does not matter). For example, how many ways can you seat people at a table? That's permutation. How many poker hands are available in five-card draw? That's a combination.</p>



<iframe width="560" height="315" src="https://www.youtube.com/embed/6J_wY6N_l7s" frameborder="0" allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe>



<p>This video is developed by David from Bionic Turtle.</p>

Probability: Permutations and Combinations

Bayes' Theorem formula, also known as Bayes' Law, or Bayes' Rule, is an intuitive idea. We adjust our perspective (the probability set) given new, relevant information. Formally, Bayes' Theorem helps us move from an unconditional probability (what are the odds the economy will grow?) to a conditional probability (given new evidence, what are the odds the economy will grow?)

Suppose your daughter tells you that her friend is coming home tomorrow. Since you don't know anything else, there is a 50% chance that the friend is a female. Now she tells you that her friend has long hair. With this additional information there are now more chances that the friend is a female. Bayes' theorem can be applied in such scenarios to calculate the probability (probability that the friend is a female.)

A simple representation of Bayes' formula is as follows:

[latex size=3]P(A/B) = \frac{P(B/A)P(A)}{P(B)} [/latex]

Where,
<ul>
	<li>P(A) is the initial degree of belief in A (probability of A).</li>
	<li>P(A/B) is the degree of belief after having accounted for B.</li>
	<li>P(B/A)/P(B) represents the support provided by B to A.</li>
</ul>


This video is developed by David from Bionic Turtle.

Baye’s Theorem

The Central Limit Theorem is a fundamental theorem of probability and describes the characteristics of the population of the means. According the Central Limit Theorem, the sample mean will be normally distributed regardless of the population distribution. Regardless of the distribution of parent.

The Central Limit Theorem tells us what happens when we have the sum of a large number of independent random variables each of which contributes a small amount to the total.


<em>
This video is developed by David from Bionic Turtle.</em>



Central Limit Theorem

This video introduces you to the concept of random variables. It is one of the most important concepts in Finance. For example this can be viewed as the outcome of throwing a die where the process is fixed by the outcome is not.

Random variables describe key things like asset returns. We then use distribution functions to characterize the random variables.

<iframe width="420" height="315" src="http://www.youtube.com/embed/IYdiKeQ9xEI?rel=0" frameborder="0" allowfullscreen></iframe>

<em>Video by Khan Academy.</em>



What is a Random Variable?

Introduction to Statistics

This frontmatter description will appear below the title

COURSE

Introduction to Statistics

LESSONS