A little dive into Discrete Distributions

Hey there, data enthusiasts! ???? In our last blog post, we cruised through the broad highways of probablity distributions . Today, we're shifting gears and zooming into the world of Discrete Distributions. Think of these as the nuts and bolts in your data science toolkit, super handy whether you're a data wiz analyzing the nitty-gritty of numbers or a decision-maker in the boardroom.

Discrete distributions are like counting cars in a parking lot - you can count them, right? ?? 1, 2, 3... just like that! They're perfect for scenarios where you can list all possible outcomes. Whether it's rolling dice (will I get a 6?) or checking how many unread emails are sitting in your inbox (too many, I bet!), discrete distributions are your go-to tool.

Let's dive into some common discrete distributions and link them with real-world examples. Buckle up, it's going to be an enlightening ride!??????

• ?? Binomial Distribution: Think of this like a series of traffic lights you encounter on your way to work. There's a chance (probability) at each light to either hit green (success) or red (failure). The Binomial Distribution helps you calculate the likelihood of hitting a certain number of green lights out of the total number you encounter. ?? So if you have 10 signals on your way and the probability of green is 50% [assume yellow you consider as Green like me] then below is the probability distribution plot.

More details on this here

• ?? Poisson Distribution: This one's like counting the number of cars that pass by your favorite roadside café in an hour. It’s perfect for modeling events happening independently over a fixed period. In data science, it's like keeping tabs on the number of times your website crashes in a month (though let's hope it's always zero!). ???Let's assume - the average number of cars passing by in an hour is 20 then below each green bar represents the probability of exactly that number of cars passing by the café in an hour, based on the Poisson distribution

A detailed article on Poisson distribution is below.

• ?? Geometric Distribution: Imagine a basketball player practicing free throws. The Geometric Distribution is all about finding the odds of how many shots they’ll take before scoring the first basket. In life, it's like flipping a coin repeatedly until you first get heads. Tails, tails, tails, and finally, heads! ??The graph below shows the likelihood of the first heads occurring on each toss, up to 20 tosses [There is only a 5% probability that you get heads on the 5th coin toss- i.e you don't know what's wrong with you]

• ???? Negative Binomial Distribution: This is the Geometric Distribution’s more ambitious sibling. Let's say a car mechanic is fixing engines, and they're interested in the number of engines they need to check before finding three that need a specific part replaced. It's about counting trials until a set number of successes. ???If the probability that an engine needs the part is 20% then, the below graph shows the probability distribution of the number of engines the mechanic needs to check before finding three that require the part.

• ??? Hypergeometric Distribution: Ever been in a lottery draw where winning tickets are drawn without putting them back in? That's your real-life example. In the car world, think of it as selecting a few cars from a lot and figuring out the probability of them being electric vehicles. ??Below graph - The total number of cars in the lot - 100, the number of electric vehicles in the lot - 20, and the Number of cars we are selecting-10, so

• ?? Uniform Discrete Distribution: This one’s simple - just like rolling a fair die. Each side (from 1 to 6) has an equal chance of coming up. It's like randomly picking a day of the week for your road trip; each day has an equal chance of being chosen. ??

Below is a diagram showing, all the variations within the discrete distribution

And there you have it! Discrete Distributions aren't just confined to the realms of data science; they're revving their engines in our daily lives too! Stay tuned for our next post where we'll shift gears into the world of Continuous Distributions. Keep calculating and stay curious! ????

Next post I will explore Continuous Distribution and its variations.

#datascience #statistics