Exponential Distribution! AWESOME EXPLANATION. Why is it called 'Exponential'?

0:00 Intro
0:49 Definition
4:41 Visualisation (PDF and CDF)
9:21 Example (with calculations)
17:05 Why is it called "Exponential"??

[harshmalik]

All of your videos keep giving me the Eureka moment at some point in the video. Keep doing what you're doing ZED. Lots of love and admiration.

[irfansayed]

Over the years, I have searched literally dozens of text books and articles to get an idea why the exponential distribution is a declining curve. This is the first instance that I have encountered a 'success' -- to use a statistical jargon. A similar reasoning explains the exponential smoothing model for forecasting, and only a couple of authors have really bothered to explain it. Great job Justin! Pretty soon, I guess you will need to revise the number of visits to your Thanks a lot!

[RD-lfpt]

Fantastic, zed statistics! This should be the number 1 option for explaining this topic out there! This is awesome (and what learning should be like). Thanks!

[bhavasindhu]

The best intuitive video on exponential distribution I have seen so far.. Thanks Justin for sharing.

[enchanted_swiftie]

This channel gets me some internel confidence that the topic I am searching for hours on the internet *will* be resolved with more than enough depth with the clarity needed.

[tommymerelte]

your voice so soothing bruh, it plug all the theories into my head perfectly

[swkim]

Justin explains exactly what I was wondering about the concept, or the big picture, about Exponential Distribution. I wanted so badly to interpret its graph, but there was no tutorial that told me about it until I reached this video. And this one is amazing! It just enlightens all that I wanted to know about this subject. Thanks a lot, Justin!

[ylu]

This video and this channel are definitely the statistics explained in an intuitive way at its best. Love it and feel fortunate to find this resource. THANK YOU!

[athar]

Brilliant teacher, very clear with a commonsense approach.

[calambuhayjr.josevirgiliog]

All I can say is Thank you from the bottom of my heart.... This saved me...

[ericfuerderer]

Clearest stats video I have ever watched. Thank you

[inamahdi]

Interesting. when you were explaining the pdf, I couldn't help but notice that behavior was similar to the geometric distribution. I wonder why.

[brennawalker]

You seriously rock! I have a test in a few days, and I have watched all of your videos regarding probability distributions. Feeling much much better! Again, thanks so much :)

[TUMENG-TSUNGF]

Another way to get an intuition for the shape of the exponential distribution would be to draw events on a number line you first draw them equal width apart (if it’s 3 hours per event then draw them one hour apart). Now sample 1 point per hour or something like that, you’ll see that the waiting times follow a uniform distribution. Now we can try to “randomize” the intervals a bit aka move the events around by for example one event 2 hours early and another 2 hours late to balance it out (so that the average rate stays the same). You can see that for the two intervals surrounding the event that’s moved two hours early, they were originally both 3 hours. Then, after the move, they become 1 and 5 hours. For the first interval, all waiting times within 1 hour still remain, on the other hand, higher waiting times between 1 and 3 hours are stripped away and converted to waiting times 3-5 hours in the second intervals. Higher waiting times have a higher chance of being converted to even higher waiting times, but lower waiting times do not. That’s why the density is higher towards shorter waiting times. I hope it makes sense.
Another even simpler way to look at it is: if we sample the waiting times once per hour, for every waiting time of 3 hours, there MUST be one sample each for 2, 1 and 0 hours between it and the next event. On the other hand, if you have a waiting time of 1 hour, there isn’t a guarantee that there exist waiting times higher than 1 hour. In general terms, an instance of a longer waiting time corresponds to one instance each of all the waiting times shorter than it; however, the opposite doesn’t hold true (an instance of a shorter waiting time doesn’t guarantee an instance of any higher waiting time). That’s why the density HAS TO decrease towards higher waiting times.

[archerdev]

pois(X) and exp(X) bless you sir for this great lecture. Wonderful.

[arunrajbhandari]

I swear bro you are one of the best teachers out there!

[sultanhaiderwadoodmufti]

Thank you just soooo much! May the lord give you paradise in this in this one and afterlife.

[yuganderu]

Sir you are sooo kind person, you didn't let us to watch the entire poisson distribution video unlike many youtubers who take advantage of this and make viewers watch multiple videos, Sir you are super. Namaskaram sir🙏🙏🙏🙏🙏

[NickHope]

The axes on the graphs could do with some explanation...
6:06 On the Poisson distribution PMF graph on the left:
- The X axis represents unique visitors to the website per hour.
- The Y axis represents the probability of each discrete number of people visiting per hour.
On the Exponential distribution PDF graph on the right:
- The X axis represents hours until next arrival.
- The Y axis does NOT represent the probability itself, which would have a scale of 0 to 1. Rather, the Y axis represents the PROBABILITY DENSITY, which is the RELATIVE LIKELIHOOD of each value on the X axis occurring. It's scale (0 to 3 in this case) is such that the total area under the graph = 1.
08:27 - On both CDF graphs, the Y axes DO represent the probability (scale 0 - 1).
10:21 until the end - The Y axis still represents the probability density (converted for minutes) and not the actual probability.
17:10 The explanation is a bit misleading. It doesn't explain why the graph falls; if the Y axis represented the probability of visitors arriving within discrete periods on the X axis, it would fall anyway, in a linear fashion, so that the product of the values on the X and Y axes remained uniform. But it does explain why the graph is CONCAVE, due the exponential nature of the function, and not linear. It's also unfortunate and confusing in this example that the PROBABILITY DENSITY at 0 minutes (0.05) is the same figure as the PROBABILITY that a visitor lands within each minute (0.05). They are not the same thing.

[aimanali]

Man i would have never understood it any other way. Outstanding explanation 👏👏👏