dbaupp comments on 2012 Less Wrong Census/Survey - Less Wrong

65 Post author: Yvain 03 November 2012 11:00PM

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Comment author: MixedNuts 04 November 2012 04:26:57PM *  5 points [-]

Intuitive answer:

Picture a horizontal line and points scattered around it. If there are many points, the line will be dark and there'll be a cloud around it. If there are few points, you'll get a vague shape and it won't be easy to tell where the line originally was.

Rigorous answer:

print [
len(filter(lambda x: x > 0.6 *per_day,
[
sum([ randint(0,1) for birth in range(0, per_day) ])
for day in range(0, 365)
]))
for per_day in (15, 45)
]

Thoughtful answer: Why would I bother thinking? Fetch me an apple.

Edit: For copulation's sake, whose kneecaps do I have to break to make Markdown leave my indentation the Christian Underworld alone, and who wrote those filthy blatant lies masquerading as comment formatting help?

Comment author: dbaupp 06 November 2012 11:31:53PM *  1 point [-]

That's not such a rigorous answer:

Imagine you have a random sample with n observations x_1, ..., x_n, independently and identically distributed according to some distribution with mean mu and variance s^2.

The sample mean is sum(x_i)/n (the expected value is mu as one would hope). Doing some manipulations we find that this has variance s^2/n, i.e. a large n means a small variance, so larger samples are more tightly clustered around mu.