And this is a slightly confusing notation, forgive me.

The smallness of that probability is what we mean by extremity.

So again each of these rows are sort of an alternate universe so if we, if we just

Italians. This is precisely meant to avoid backlashes.

It's your probability of rejecting the null when in fact you should.

What's the probability of the joint X, Y?

In this case, there's only one such variable, Cloudy.

Question 1 In the first question, I'm going to ask you some very basic probability questions.

Then the value of the state for the action go up would be obtained as follows.

Probability

Phil, the odds against

And it makes much more sense to talk about the probability or random variable equaling a value, or the probability that it is less than or greater than something or the probability that is has some property

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

It's kind of the big thing in application and machine learning.

Then I just normalize.

What are the odds?

If you try to do it yourself you have to be aware of precision problems with your input data.

What's nice is given the assumptions of the normal distribution and using normalized scores, we know the probability of winding up in one of those four boxes or we can estimate them.

That is not the case for song.

Let's use the Laplacian smoother with K 1 to calculate the few interesting probabilities

Probability of success

Probability of failure

Of course it has no clue that it is exactly over here.

This represents the set of all the cubes.

Let's just check, and as predicted, almost all cells have a probability of 0.03.

And these are mutually exclusive events, you can't have both of them

And comparing heights of the tallest building in two cities, that's a deterministic number.

You might say OK, that's the probably of getting exactly 1 times the probability of getting 2 out of 3 plus the probability of getting 3 out of 3.

What's the probability of the complement?

We now apply Bayes rule.

And here is my answer. You can really read off the formula that I just gave you.

If I pick a random T value, if I take a random T statistic

There's going to be a 10 percent chance you get a pretty good item.

Now let's have something a little bit more interesting.

Frack the odds.

Equally possible,

Now this format begins to look very much like the game tree that we talked about in the previous unit.

He estimated a probability that we will fail to survive the current century

They cannot happen at the same time.

This is being answered using Bayes rule, so this is the probability of being happy given that it rains times the probability that it rains over the probability of being happy.

Use Laplacian smoothing with k 1 to compute the probability of a movie being old this is a prior probability, which is just based on class counts the probability of the word top as a title word in the class of old movies, and the probability that a new movie that we look at by new I mean a movie we've never seen before that is called top, the probability this movie that corresponds to the old movie class with the new movie class.

Here we're given a marchov chain between A and B, with the transition of A to itself is 0.9 with 0.1 chances transitions to B.

Now, this statement is not true.

If I keep expanding this, I get the following solution.

One more quick game tree to evaluate.