[+] Complete mathjax fonts

src/report/report_document.md

@@ -46,9 +46,11 @@ Since there are many outliers, medians and IQR will more accurately represent th
 
 ## COVID-19 Popularity Ratios
 
-Then, we analyzed the popularity ratio of COVID-related posts for our three samples. The popularity of a post defines how much other people are interested in the post, measured by the total number of user interactions (likes and comments) on that post. From that data, the relative popularity ratio for COVID-related posts calculates how popular are COVID-related posts compared to all other posts, calculated by the equation, which is a ratio of the average popularity of both: 
+Then, we analyzed the popularity ratio of COVID-related posts for our three samples. The popularity of a post defines how much other people are interested in the post, measured by the total number of user interactions (likes and comments) on that post. From that data, the relative popularity ratio for COVID-related posts calculates how popular are COVID-related posts compared to all other posts, calculated by the equation, which is a ratio of the average popularity of both:
 
-$$\left(\frac{\sum\text{Popularity of COVID-posts}}{\text{Number of COVID-posts}}\right) / \left(\frac{\sum \text{Popularity of all posts}}{\text{Total number of posts}}\right)$$
+<blockquote>
+$$ pop_{user} = \left(\frac{\sum\text{Popularity of COVID-posts}}{|\text{COVID-posts}|}\right) / \left(\frac{\sum \text{Popularity of all posts}}{|\text{All posts}|}\right)$$
+</blockquote>
 
 There are three divisions in this equation, so there are three possible places where it might divide by zero. So, to prevent division by zero, we ignored people who didn't post about COVID-19 or didn't post anything at all, and we also ignored people who have literally 0 popularity on any of their posts. In our data, we ignored this amount of people for each sample:
 
@@ -71,9 +73,12 @@ After we answered how frequently people posted about COVID-19 and how interested
 
 ## Method
 
-In this analysis, we defined the start of COVID-19 as `2020-01-01` and ignored all posts prior to this date. Then, we split the dataset into intervals of 7-days for every day since `2020-01-01`, and calculated the frequency and popularity of that interval, which gave us a list of numbers `x` where:
-
+This analysis is separate for each of our samples, just like the previous analysis. However, unlike how tweets are separated for each user in the previous analysis, we combine the tweets of all users in each sample in this analysis. In this analysis, we defined the start of COVID-19 as `2020-01-01` and ignored all posts prior to this date. Then, we calculate the average frequency and popularity ratio for every day since `2020-01-01`. To reduce random variability, instead of using only the data from the day in the calculation, we used the average of the last 7 days for each day, and calculated the frequency and popularity of that interval. This calculation gave us a list of numbers `freqs` and list of dates `dates` where, for every date `dates[i]`,
 
+<blockquote>
+$$ \text{freqs}_i = 
+\sum_{j = 0}^{7} \frac{|\text{COVID-posts on dates}_{i - j}|}{|\text{All posts on dates}_{i - j}|} $$
+</blockquote>
 
 **_TODO_**