Mean of the distribution

Linear middle of the distribution

Mean value of the normal distribution

What I want to do in this video is to generalize it.

MV is the linear middle of the distribution.

It's one standard deviation in the distribution of sample means. So this distribution of sample means, again.

Mean value of the standard logarithmic distribution

That's called a probability histogram.

That's largely influenced by the sample size.

Here's a quiz for you.

They'll fluctuate, right.

Finally the shape of this distribution of sample means will be approximately normal even if the distribution in the population isn't normal.

Here is an example of a particular cluster, where different contours show, say, average distribution of galaxy light, or the number density, or the inferred galaxy mass, or mass distribution for the whole cluster.

The three main principles are what we just we worked through.

So an extractor is something that takes a bumpy distribution and makes it into a uniform distribution over the key space.

And, again we don't know most, most of the time if the distribution in the population is normal.

Let's start with 2 Gaussians and say they have identical variances. Let's multiple them.

The prior has a mean of mu and a variance of sigma squared.

Suppose you're localizing another vehicle, and you have a prior distribution that looks as follows.

So there's about 86 billion neurons in our brain.

So you know a distribution is perfectly normal if it's, if it has this bell shape and if it's symmetrical around the mean.

There's a 95 chance that the true population mean, which is the same thing as the mean of the sampling distribution of the sample mean, there's a 95 chance, or that we are confident that there's a 95 chance, that it will fall in this interval.

So pretty straightforward.

From the mean to one standard deviation above, and one standard deviation below.

I know that's a mouthful. So, you might wanna replay that.

So the T statistic that we could derive from that is going to be our mean, 17.17 minus the true mean of our population.

If the operators had instead rolled dice to decide their initial rotor positions, the starting points in the sequence could have been uniformly distributed.

I finally want to teach you about the concept of a standard score.

Let's just go back to our example and see what an amazing thing you've just programmed.

I'm giving you a skeleton program, which has a function update, that takes as an input a mean and a variance for the first distribution and a mean and a variance for the second distribution and outputs the new mean and the new variance of the product of those.

If the probability distribution of x is Gaussian, it would mean Mu and variant sigma squared, then we'll write this as x the random variable tilde.

I've got in my example minus the mean, minus the center, minus the mean of distribution.

Here, I said samples equal to 30 or greater, some people would be a little more liberal then that and say if you have samples of even twenty or greater you'll get a normal distribution.

Suppose our mean is 10 and 13, and the variances are imbalanced 8 and 2 which corresponds to the following picture.

Intuitively speaking, this is the case because we actually gain information.

And if you look at the data, when you have that kind of a structure, you get a very even distribution of the shops and the physicians and the pharmacies and the cafes in Paris.

And this is my histogram of a Gaussian with mean minus 6.

But now we'll look at histograms that represent distributions of samples.

Suppose I use the following Gaussians μ 10, σ 2 4, ν 12, r 2 4

Suppose we multiply two Gaussians as in Bayes rule a prior and a measurement probability.

But remember the wand, the infra red meter, runs a little hot.

You can see areas where neuronal cell bodies are being stained.

There's variance in the sample SD squared.

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