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The only outcome that satisfies this is the TTT outcome.

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In fact, the probability of any exact price is really low. So discrete probability.

## Probability distributions for discrete random variables

Two fair dice are rolled at once. Cut and paste.

Well, let's see. Continuous probability distribution for continuous random variables.

So three out of the eight equally likely outcomes provide us, get us to one head, which is the same thing as saying that our random variable equals one. So there's only one out of the eight equally likely outcomes that meets that constraint.

### The mean and standard deviation of a discrete random variable

Ot could have tails, tails, he. To make this more concrete, we will use the diamond dataset from ggplot2 to illustrate this example. So you could get all he, he, he, he.

The concept of expected value is also basic to the insurance industry, as the following simplified example illustrates. The x-axes shows givs different outcomes of the random variable while the y-axes shows the corresponding probabilities of these outcomes You might sometimes see the term probability distribution table. This outcome would get our random variable to be equal to two. Well, for X to be equal to two, we must, that means we have two he when we flip the coins three times.

Bead just like that.

## Probability distributions and their mass/density functions

And then you could have all tails. What's the probability that the random variable X is going to be equal to two?

While probability density functions pdf are used to describe continuous probability distributions. A manufacturer receives a certain component from a supplier in shipments of units.

### Continuous probability distributions

Just like that. If either one of the units is defective the shipment is rejected. We have this one right over here. X could be two. And I can actually move disrete two in actually as well. When the outcomes are discrete we have the ability to directly measure the probability of each outcome. And now we're just going to hsad the probability. And there you have it! Which of these outcomes gets us exactly one head?

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I'm using the wrong color. Compute the standard deviation of X. So let's think about all of Lookinh different values that you could get when you flip a fair coin three times.

It's one out of the eight equally likely outcomes. I can write that three.

### Not like an algebra variable

Discrefe this means is that they are assuming the data being generated comes from a particular well studied distribution. So what's the probability, I think you're getting, maybe getting the hang of it at this point. And then we can do it in terms of eighths. You could have tails, head, tails.

## Random variables

So cut and paste. So Looklng half. It can't take on any values in between these things. And then finally we could say what is the probability that our random variable X is equal to three? We have that one right over there. So what's the probably that our random variable X is equal to zero? We can visualize this particular pmf as follows: library "ggplot2" library "dplyr" prob.

The only outcome that satisfies this is the TTT outcome.

Let X denote the difference in the of dots that appear on the top faces of the two dice.