We'll let R do the work.

And of course the answers is 0, if p 0, the coin comes up tail all the time and as a result it won't vary, therefore there is no variance.

It moves on average by 1 to the right so the mean is going to be 1.

We take the product of the variance of x and the variance of y modally with the normalizers and we get something quadratic even in variance space.

12.4 is much closer to 13 than 10, and that's because the Gaussian centered on 13 has a much narrower variance than the one on 10.

Is there any way to pull out this uncertainty from our omega matrix?

It takes our data and returns a single number, which is the variance of the data.

Now the mean is obviously 50, 0.5100, the variance will be 25, 1000.25.

At 10 they also just both multiply.

In this case it's the same, and in this case it's 0.

Now what is going to be the variance?

Did it touch the bone?

If you take 1 4 plus 1 4, then you get 1 2, so 1 over 1 3 equals 2, which means the new variance term is half the size of the previous variance terms.

That's the same as σ 2 over 2, which means a new variance squared is half of the old one.

As we know, this gives us an estimated mean.

And we're going to want to square this as well.

The way you get that is divide the 6618 by 83. How about the variance?

Obviously there are outliers in that data.

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

It's something that I have to do with other people.

Measurement Update So question 1 is measurement update.

Let me ask the hard question now.

We're going to use these throughout this entire course are standard deviation and variance.

What is the youngest person to earn 267,000 in our data set?

In a population with a mean height of 70 inches and a variance of 25, what are the mean and variance of the distribution of heights in centimeters?

Without telling you why I'm doing this, I want to see what the effect is.

When we square them, they will be 25 times as large.

We're more interested in the Bi Directional Scattering Distribution Function. This type of function captures both how light reflects from and transmits through material.

That's largely influenced by the sample size.

Power is multi polar.

The mean is now a vector with 1 element for each of the variance.

But a lot more, going forward in the class.

The mean is easily calculated it's 2 and 4.

Just for the exercise of applying the formula, compute for me the mean and the variance.

Well, you might vaguely remember that the sum of two coin flips or sum of any two of anythings you do, the variances just add up.

And we know that our variance is essentially the probability of success times the probability of failure.

Then by following the protocol, the receiving device knows how to put it all back together.

That's just dividing by N.

You're welcome, sir. Fall out.

The answer is 0.72.

Dispersion

Variance

So the standard deviation of the Ys is 6.

There are 4 possibilities 0 and 0, 1 and 0, 0 and 1, and 1 and 1.

Consider the case where a number can be either 0 or 1 with 0.5 probability for each.