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

And, yes, the answer is 0.108.

And using the prior, we know that P of not C is 0.99.

Just to check suppose probability of cancer is 0.1, the sensitivity is 0.9, specificity is 0.8.

So if you get a positive test result you're going to raise the probability of having cancer relative to the prior probability.

Here you get 0.72, which is the product of not having cancer in the first place 0.9 and the probability of getting a negative test result under the condition of not having cancer.

We now apply Bayes rule.

Now let me ask you a really tricky question.

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

For A, it's 0.1 for X and 0.9 for Y.

R. For now, power is simply the probability that you'll reject the null hypothesis when in fact you should.

And here's my code, this implements Bayes rule.

Now that one comes up with heads at 0.9.

In this video we talked about how to estimate p of x, the probability of x, for the purpose of developing an anomaly detection algorithm.

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

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

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

And the answer is 0.45.

What I want you to compute for me is the probability of the second test to be positive if we know that the first test was positive.

Now, what's remarkable about this outcome is really what it means.

So now I want to ask you a really tricky question

For coin X, we know that the probability of heads is 0.3.

The bottom row's more difficult, and we'll estimate those probabilities based on power.

So, even though I received a positive test, my probability of having cancer is just 4.3 , which is not very much given that the test itself is quite sensitive.

So 0.5 times 0.95 gives you 0.45 whereas the unfair coin, the probability of tails is 0.1 multiply by the probability of picking it at 0.5 gives us 0.05

Secret carries 1 3, is 1 9, and secret 1 3 again.

In our cancer example, we know that the prior probability of cancer is 0.01, which is the same as 1 .

And what's the same for P( C, Neg).

Specifically, the joint probabilities.

The probability of a positive test and having cancer.

And once again, we'd like to refer the corresponding numbers over here on the right side 0.1 for the cancer times the probability of getting a negative result conditioned on having cancer and that is 0.1 0.1, which is 0.01.

It really gives me a 0.8 chance of getting a negative result if I don't have cancer.

And coin 2 is also loaded.

So there's 2 total events.

let's look at some actual random variable definitions.

Now, I'm going to make it really difficult. I'm going to give you a coin let's call it loaded.

Now comes the hard part

So let's say I want to figure out the probability I'm going to flip a coin eight times and it's a fair coin.

And see what happens. It multiplies.

Now, this statement is not true.

Now, let's do one last modification and let's write this procedure assuming you observed a negative test result.

Now, what you do, you add those up and then normally don't add up to one.

Then we can flip and get heads or tails for the coin we've chosen. Now what are the probabilities?

This is a probability of a positive test given cancer.

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