Really, this is all we are doing, but let’s make some sense of it.

Well maybe yesterday was confusing, maybe it wasn’t. In any case, today *should* clarify some things for you if you are confused and should make things more clear if you are not. Today we are going to go over a quick example of what a function involving one random variable looks like. Now you may notice I keep saying one, that’s because you can technically have as many variables as you want, but since this is fairy complex stuff, let’s just stick with the one for now.*

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October 2, 2019 | Categories: 365 Days of Academia | Tags: Borel, cumulative distribution function, education, Function of random variables, math, mathematics, Poisson, probability, probability density function, random variables, statistics | Leave a comment

Yep we’re getting a little complicated, but let’s see if we can make sense of this.

Now that we’ve looked at conditional probabilities we can talk about other things we can do with random variables. If you’ve been keeping up with us so far, then this shouldn’t be too crazy of an idea, really all we are going to do today is take a random variable and transform it somehow. Interested? Let’s go!*

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October 1, 2019 | Categories: 365 Days of Academia | Tags: Borel, cumulative distribution function, education, Function of random variables, math, mathematics, Poisson, probability, probability density function, random variables, statistics | Leave a comment

How does this not exist on the internet?! This is directly from my book, so it looks a little… well loved.

Up to now we’ve been dealing with single variable pdf and the corresponding CDF. We said that these probabilities relied on the fact that our variable of interest was independent. However, what if we knew some property that impacted our probability? Today we are talking conditional probability and that is the question we will be answering. It’s going to be a long, long post so plan accordingly.*

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September 30, 2019 | Categories: 365 Days of Academia | Tags: conditional probability, cumulative distribution function, education, math, mathematics, Poisson, probability, probability density function, random variables, statistics | Leave a comment

Maybe we shouldn’t phrase it this way, since there is still quite a few days left of 365DoA, but you made it to the end! No, not THE end, but if you’ve been following along the past few posts we’ve introduced several seemingly disparate concepts and said, “don’t worry they are related,” without telling you how. Well today, like a magician showing you how to pull a rabbit from a hat, let’s connect the dots and explain why we introduced all those concepts!*

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September 29, 2019 | Categories: 365 Days of Academia | Tags: binomial distribution, cumulative distribution function, education, gaussian, math, mathematics, normal distribution, Poisson, probability, probability density function, random variables, standard deviation, statistics | Leave a comment

Poisson’s return!

You have all been really patient with seeing how we tie these last few posts together and frankly I think that we are on track to do that in the next post. Today however we have one more thing to introduce then we can bring it all together, that would be yet another normal (again we usually refer to this as

the gaussian) distribution. If you recall I hinted at this a few days ago in the

Poisson pdf post. Let’s look at what this means and why we would want to use this.*

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September 28, 2019 | Categories: 365 Days of Academia | Tags: binomial distribution, cumulative distribution function, education, math, mathematics, normal distribution, Poisson, probability, probability density function, random variables, standard deviation, statistics | Leave a comment

The Poisson distribution changes shape as λ changes

Well in an effort to catch up to what we’re currently learning in my class today we should hammer out the Poisson distribution so we can get to combining some ideas. The interesting thing about this distribution as you can see from above, is that as we adjust λ the shape of the distribution changes. Let’s get started.*

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September 26, 2019 | Categories: 365 Days of Academia | Tags: cumulative distribution function, education, math, mathematics, Poisson, Poisson distribution, probability, probability density function, random variables, standard deviation, statistics | Leave a comment