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Discrete and continuous random variables. Constructing a probability distribution for random variable.
Constructing probability distributions. Probability models example: Probability models. Valid discrete probability distribution examples. Probability with discrete random variable example.
Probability with discrete random variables. Mean expected value of a discrete random variable. Expected value.
Variance and standard deviation of a discrete random variable. Standard deviation of a discrete random variable. Next lesson. Current time: Probability distributions of random variables. Video transcript What I want to discuss a little fr in this video is the idea of a random variable.
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And random variables at Sexy Rotterdam african indian cougars can Looking for quick easy and discrete a little bit confusing because we will want to think of them as traditional variables that you were first exposed to in algebra class. And that's not quite what random variables are. Random variables are really ways to map outcomes of random processes to numbers.
So if you have a random process, like you're flipping a coin or you're rolling dice or you are measuring the rain that might fall tomorrow, so random process, you're really just mapping outcomes of that to numbers. You are quantifying the discrfte.Sexy Women Wants Real Sex Norway
So what's an example of a random variable? Well, let's define one right over here.
So I'm going to define random variable capital X. And they tend to be denoted by capital letters. So random variable capital X, I will define it as-- It is going to be equal to 1 if my fair die rolls heads-- let me write it this way-- if heads.
And it's going to be equal to 0 if tails.
I could have defined this any way I wanted to. This is actually a fairly typical way of defining a random variable, especially for Lolking coin flip. But I could have defined this as And I could have defined this as And this would still be a legitimate random variable.
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It might not be as pure a way of thinking about it as defining 1 as heads and 0 as tails. But that would have been a random variable.
Notice we have taken this random process, flipping a coin, and we've mapped the outcomes of that random process. And we've quantified them.
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We can define another random variable capital Y as equal to, let's say, the sum of rolls of let's say 7 dice. And when we talk about the sum, we're talking about the sum of the let me write Looking for quick easy and discrete the sum of the upward face after rolling 7 dice.
Once again, we are quantifying an outcome for a random process where the random process is rolling these 7 dice and seeing what sides show up on top. And then we are taking those and we're taking the sum and we are defining a random variable in that way.Adult Want Nsa Newton Highlands Massachusetts 2161
So the natural question you might ask is, why are we doing this? What's so useful about defining random variables like this? It will become more apparent as we get a little bit deeper in probability.
But the simple way of thinking about it is as soon as you quantify outcomes, you can start to Looking for quick easy and discrete a little bit more math on the outcomes.
And you can start to use a little bit more fro notation on the outcome. So for example, if you cared about the probability that the sum of the upward faces after rolling seven dice-- if you cared about the probability that that sum is less than or equal to 30, the old way that you would have to have fpr it is the probability that the sum of-- and you would have Looking for quick easy and discrete write all of what I just wrote here-- is less than or equal to You would have had to write that big thing.
And then you would try to figure it out somehow if you had some information. But now we can just write the probability that capital Y is less than or equal to Sex dating in Rexmont It's a little bit cleaner notation. And if someone else cares about the probability that this sum of the upward face after rolling seven dice-- if they say, hey, what's the probability that that's even, instead of having to write all that over, they can say, well, what's the probability that Looking for quick easy and discrete is even?
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Now the one thing that I do want to emphasize is how these Looking for quick easy and discrete different than traditional variables, traditional variables that you see in your algebra class like x plus 5 is equal to 6, usually denoted by lowercase variables. These variables, you can essentially assign foor.
You either can solve for them-- so in this case, x is an unknown.
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You could subtract 5 from both sides and solve for x. Say that x is going to be equal to 1. In this case, you could say, well, x is going to vary.
We can assign a value to x and see how y varies as a function of x. You can either assign a variable, you can assign values to them. quidk
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Or you can solve for them. You could say, hey x is going to be 1 in this case. That's not going to be the case with a random variable. A random variable can take on many, many, many, many, many, many different values with different probabilities.
And it makes much more sense to talk about the probability of a random variable equaling a value, or the probability that it is less than or greater than Looking for quick easy and discrete, or the probability that it has some property. And you see that in either of these cases.
In the next video, eas continue this discussion and we'll talk a little bit about the types of random variables you can have.