Name: 中心極限定理｜推理統計｜概率與統計｜可汗學院 (Central limit theorem | Inferential statistics | Probability and Statistics | Khan Academy)
Uploaded: 2021-01-14T07:53:58.000Z
Duration: 9 min 49 s

In this video, I want to
talk about what is easily

情態副詞

one of the most fundamental and
profound concepts in statistics

with any distribution that
has a well-defined mean and

variance-- and if it has
a well-defined variance,

it has a well-defined
standard deviation.

And it could be a continuous
distribution or a discrete one.

I'll draw a discrete one,
just because it's easier

to imagine, at least for
the purposes of this video.

So let's say I have a discrete
probability distribution

to make it look anything close
to a normal distribution.

Because I want to show you
the power of the central limit

Let's say it could take
on values 1 through 6.

You have a very high
likelihood of getting a 1.

Let's say it's an OK likelihood
of getting a 3 or a 4.

And let's say it's very
likely to get a 6 like that.

So that's my probability
distribution function.

If I were to draw a
mean-- this the symmetric,

so maybe the mean would
be something like that.

But that's my discrete
probability distribution

Now what I'm going to do
here, instead of just taking

described by this probability
distribution function,

the frequency of the
averages that I get.

Let's say my sample size-- and
I could put any number here.

But let's say first off we try a
sample size of n is equal to 4.

And what that means is I'm going
to take four samples from this.

So let's say the first
time I take four samples--

so my sample sizes is
four-- let's say I get a 1.

So that right there is my
first sample of sample size 4.

I know the terminology
can get confusing.

Because this is the sample
that's made up of four samples.

But then when we talk about the
sample mean and the sampling

distribution of the
sample mean, which we're

going to talk more and more
about over the next few videos,

normally the sample refers
to the set of samples

And the sample size tells
you how many you actually

But the terminology
can be very confusing,

because you could easily view
one of these as a sample.

And what I'm going to do is
I'm going to average them.

So let's say the mean-- I
want to be very careful when

The mean of this first
sample of size 4 is what?

That is my first sample mean
for my first sample of size 4.

My second sample of size 4,
let's say that I get a 3, a 4.

I just didn't happen
to get a 6 that time.

So for the second
sample of sample size 4,

my second sample mean is
going to be 3 plus 4 is 7.

want to make it clear
what we're doing here.

Actually, we're going
to do a gazillion more.

So let's say my third
sample of sample size 4--

so I'm going to
literally take 4 samples.

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中心極限定理｜推理統計｜概率與統計｜可汗學院 (Central limit theorem | Inferential statistics | Probability and Statistics | Khan Academy)

literally

weird

assume

approach