We're a little crazy, about science!

Posts tagged “math

Day 62: Two Random Variables A2

Like we did with question 1, this will be the solution to the question we posed in the last post, if you haven’t tried to solve it yet, go give it a shot. If you have and are dying to check your answer, then let’s look at the solution.*

(more…)


Day 61: Two Random Variables Q2

For those of you who have been following along, today we are going to post another question and in the next post we will give the solution. This will be another two random variable question and we’ve covered everything you need to solve it in our previous posts. So with that, let’s get to today’s question.*

(more…)


Day 60: Two Random Variables A1

Hopefully if you’re reading this you saw our last post, where we gave the question we will solve today. If you haven’t had a chance to try and solve it, please feel free to stop and give it a shot. If you’re ready to see how we solve it, then let’s get started.*

(more…)


Day 59: Two Random Variables Q1

Well now that we’ve had a minute to take a breath, let’s try out something new. In this post I will give the question and in the next post we can work out the answer. For those of you playing at home, this will be a good way to check your knowledge and for me, it will give the the chance to do the same.*

(more…)


Day 56: One Function of Two Random Variables Example 3

Example1

Today we are solving this guy!

Okay quick example, still not super difficult, but one we can work out to a complete solution. We’ve gone over a few examples now, but we’re going to go over a few more for both my benefit and yours. So let’s dive in.*

(more…)


Day 55: One Function of Two Random Variables Example 2

resturant

Don’t worry, the image ties into what we are doing today, I promise!

Well our last post we took a break and talked zombies! While I would love to do a whole month of halloween topics, this year is not the time, maybe next year. In any case today we are going to go over another example of a single function of two random variables. This is going to be slightly more complex than our first example, however it won’t be extremely complex (we’re working towards it). So let’s take a look shall we?*

(more…)


Day 53: One Function of Two Random Variables Example 1

One Function of Two Random Variables

Hopefully at this point we’ve demystified more than just a few concepts at this point. Today we are going to look at one function of two random variables. Originally I was going to break into a joint CDF example that involved dependent variables, but it turns out my book doesn’t cover that! Oops, guess I should’ve read ahead. In any case let’s talk functions!*

(more…)


Day 52: Joint Cumulative Distribution Function Example 1

JointCDF.png

We’re getting into some interesting things today!

Well here we are again, today we are talking functions of two random variables. If you’re looking for the beginning, this isn’t it, but you can read the introduction here. If you’ve kept up, then you’re ready to go over the example we have today, so let’s get started.*

(more…)


Day 51: Joint Cumulative Distribution Function

Joint CDF Image

As promised, today we are going to talk about two random variables that are not independent. This means that the individual probabilities don’t sum to be equal to the joint probability (like they did yesterday). Like our normal CDF, we can find a CDF for two random variables, but let’s take a look at how this works.*

(more…)


Day 50: Intro to Two Random Variables

Coins

I was debating about not posting anything today. It’s been a bit rough for me these past few days. However, I’m going to write a little something today and tomorrow to introduce two random variables (so we don’t skip a day). This is going to be a lot like our single random variable examples, but (of course) more complex, let’s take a look at what I mean.*

(more…)


Day 49: Functions of One Random Variable Example Part 5

function of RV fourth example5

Let’s look at something a bit different today!

If you’ve been following along, we’ve been taking it easy the past few days. I’ve also been going over (relatively) simple examples, so today we’re going to take a more complicated example and work through solving it. I may go over a few more examples to be honest, only because this is important to what comes next, after we nail this down, we’re going to get into functions of two random variables and as you can imagine that’s a little more complicated (a lot more).*

(more…)


Day 48: Functions of One Random Variable Example Part 4

function of RV thrid example8

A simpler example than yesterday.

Still feeling under the weather, but the show must go on as they say. So today let’s look at another example of how to solve functions of one random variable. Today will be another shorter post, but as usual I’ll try to explain everything step by step and hopefully you’ll see the methodology behind solving these types of problems.*

(more…)


Day 47: Functions of One Random Variable Example Part 3

function of RV second example

Let’s solve this guy.

Bad news readers, I’m feeling a bit under the weather. Today we’re going to go over a quick example. It’s not the one I had in mind, but it’s fairly straightforward and should help make some more sense of everything we are covering. When I start feeling better we can get into some of the newer concepts.*

(more…)


Day 46: Functions of One Random Variable Example Part 2

bayes theorem joke

Another Joke by xkcd

As promised today we are going to look at another example of how to solve functions with one random variable. If you haven’t you may want to start with our first post on the subject here.  For those of you who are caught up, let’s get started.*

(more…)


Day 45: Moment Generating Functions

distribution park joke

There wasn’t a good visual for what we are talking about today, so how about a joke instead?

Well from the views it looks like my function of a random variable example was a big hit. Hopefully we’re clearing a lot of the confusion up now that we are looking at some examples of how to solve these and we can get a better grasp of how this works. Today we’re going to introduce a new concept, this one is going to be a bit more complex than our last, so you may want to review our last post before we start.*

(more…)


Day 44: Functions of One Random Variable Example Part 1

func of RV

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.*

(more…)


Day 43: Introduction to Functions of One Random Variable

Function of one random variable (Borel)

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!*

(more…)


Day 42: Conditional Probability

Conditional probability pdf plot

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.*

(more…)


Day 41: Connecting the Concepts

catinthebag

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!*

(more…)


Day 40: The Normal Approximation (Poisson)

Poisson vs Gaussian

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.*

(more…)


Day 39: The Normal Approximation (De Moivre-Laplace)

Binomial_distribution plot

The binomial distribution, don’t worry we’ll get into it.

Well we haven’t covered the binomial distribution, but it should be vaguely familiar if you’ve been keeping up, specifically if you’ve already read about the gaussian pdf. Today we are going to talk about what the binomial distribution is and how it relates to the normal distribution. So let’s get into it and see how it relates to some of the topics we’ve been covering!*

(more…)


Day 38: The Poisson Distribution

poisson

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.*

(more…)


Day 37: Bayes’ Theorem

bayes light

We’re talking Bayes for days.

Okay, it looks like we have our topics for the next few posts and today we need to introduce something called Bayes’ rule (or theorem) if we are going to get into some of the things I want to talk about. We also need to talk about the Poisson distribution eventually, but we’ll get to that in time. For now, let’s talk Bayes!*

(more…)


Day 36: The uniform pdf

Uniform distribution

The uniform distribution, a very simple looking distribution indeed.

Today we are going to take it a bit easy, after all we still have 329 days of blog posts and not every one has to be a novel. That is why today we are introducing something called the uniform distribution. Ever wonder what would happen if nothing really mattered? Well you’re in for a treat! Let’s get started.*

(more…)