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Biased Statistics

In a video (pictured above) I was click-baited into watching, there is an interesting statistic that "1 in every 5 Americans either has had or knows someone who has had bed bugs." In an article that I read, the average American knows 600 people. I will use the assumption that each person knows 100 "famous people," none of which have or have had bed bugs. Given these two facts, how could one calculate the number of Americans who actually have bed bugs assuming that every person knows exactly 500 people and each individual is known by 500 other individuals.

Bonus: how would the results change if the number of people who know a random person was a skewed right distribution with a mean of 500?

Note by Trevor Arashiro
1 month, 2 weeks ago

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If every person with bed bugs is known by 500 other people, then 2,500 people can potentially be made to satisfy this requirement if only 1 has bed bugs. (Really it would be 501*5 = 2505 because you need to include the person who has had beg bugs but 500 is an estimate anyways) Of course, this is the worst- case scenario.

I will assume that everyone knows other people at random, which is VERY not true. In this case, people with bed bugs would know someone with bed bugs 1/5th of the time. Surprisingly, this seems to do almost nothing to the number, only reducing it by 1 to 2504.

I don't really know how to do much else but that's my analysis

EDIT: I forgot to account for people who know 2 people with bed bugs. This is going to be 1/25 people, or 100 per person with bed bugs. I think this actually makes it worse, 2,600. I'm sure this number is worse than it should be. Alex Li · 1 month, 1 week ago

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@Alex Li I've done a little work on this and posted a problem on it here.

I'm having problems simulating the most random case, where no two people are known by two other people (posted here). Trevor Arashiro · 1 month, 1 week ago

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