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We can get productivity up.

It's like designing a building before you set out to build it.

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.

For example, p might be 0.5.

So we divide by the total weight of all particles, and we get out those probabilities over here.

From that you can easily calculate the probability of measuring 'white', if a particle falls on a black square.

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

And this expression equals 0.6080 and so the probability that we have the same coin is simply the probability that we both have type 1 or fair coins, plus the probability of my having coin 2 times the probability of your having coin 2.

What do I mean by that?

We now apply Bayes rule.

It's time for some problems now,

So, there is a 1 6 probability of rolling a 1.

Basically, as far as I can tell, there are only three.

The answer is 1 4.

A candidate in election might have a true chance that any given voter votes for him.

Then lift your shirt. Show me you're not wearing a wire.

There's a 0.1 chance I might still be grumpy for some other reason.

To change this example even further.

I admit, business has been slow.

So that tells us the probability of a given b times the probability of b, is equal to the probability of b given a, times the probability of a.

My second test, after seeing a positive test, has now an increased probability of about 23 of coming in positive.

I must be frank, Your Majesty.

And slowly, slowly we're bringing it up to a moderate savings rate.

Well let's define one right over here so I'm gonna define random variable capital X and they tend to be denoted by capital letters so random variable capital X, I will define it as is going to be equal to 1 if my fair coin rolls heads and it's going to be equal to 0 if tails

Then we graph the binomial just like before.

Okay, we're gonna need identification. Keep your hands where we can see them.

Well, only 1 of them meet my conditions that right there.

What have you learned? Well, to flip a coin n times one for k small or equal to n.

What kind of odds would you have give you and me?

The probability of any random variable Y can be written as probability of Y given that some other random variable X assumes value i times probability of X equals i, sums over all possible outcomes i for the (inaudible) variable X.

This is just the theorem of total probability or forward propagation rule applied to this case over here, so nothing really new.

And then the utility of the game is the expected value, so we look at all the outcomes and the probability of each outcome.

So let's look at this, let's look at a population where the probability of success we'll define success as 1 as having a probability of p, and the probability of failure, the probability of failure is 1 minus p.

With the Central Limit Theorem, things become really easy.

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I can get heads and tails on the first as well, so the probability of heads on the first flip X Probability of getting heads on the second flip.

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.

However, if I now divide, that is, I normalize those non normalized probabilities over here by this factor over here,

On the second state we know that the probability of R is 0.6 and therefore, the probability of sun is 0.4, and we compute the probability of rain on day 2 using total probability.

It's easy to see that the probability of heads in step 2 is the probability of heads in step 2 conditioned on heads in step 1 times probability of heads in 1 plus, that's the sum, probability of heads in step 2 given we had tails in step 1 times probability of tails in step 1.

least maybe it doesn't make intuitive sense just yet, but I showed you that the probability of a and b is equal to the probability of a given b times the probability of b.

The motions don't move at all, move right, move down, move down, and move right again.

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

The probability of observing X and Y depends on what state the hidden markov model is in.