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 website!!!!! Thanks a lot!
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!
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.
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!
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!
Because 0.95 keeps getting multiplied by itself in the function. In other words, it is a constant being raised to a power, which is the nature of an exponential function.
Would have been nice to state that the y-axis on the exponential dist is lambda for the PDF and a percentage for the CDF. Unlike the Poisson Dist as both are in percentage. This confused me as I wasn't sure what the Y axis meant. I naturally thought percentage and was wondering why nothing was adding up correctly especially at 16:44 - I was like, it should equal 0.025 or 2.5% which is of course wrong. I watched the whole video with the wrong assumption haha
- The Y axis on the exponential distribution PDF does not represent Lambda (nor the probability). It actually 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. But you're right that this was not explained at all in the video. - The Y axis on the exponential CDF and the Poisson distributions is probability, on a scale of 0 to 1, and not percentage, which would have a scale of 0 to 100.
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 :)
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.
The last problem was just a fantastic one. First you treat it as an exponential distribution, so the probability of within one min becomes your probability of success. Then you treat it as geometric distribution. Brilliant!
This is a kind request to have a video series on Permutation, Combination ,Probability and Calculas. I must say your videos are very awesome. The way you explained things is fantastic. Thanks Justin
Thanks for the wonderful explanation. Just one confusion in the section "Visualisation (PDF and CDF)" - the Exponential distribution graph at @6:35 minutes is correct? because on the Y-axis you have put values greater than 1. but shouldn't these values be less than 1 representing the probability?
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.
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🙏🙏🙏🙏🙏
Saving lives. My lecturer and textbook use lambda as both the Poisson mean and Exponential mean. Can't begin to explain how many hours I wasted not realising they were referring to two different means. Thought I was losing it. Was ready to drop out of math and try my luck in humanities.
TH-cam algorithms must be pretty good that it didn’t take me long to find this video on exponential distribution >< This one answered my question exactly which is why the exponential pdf looks like the way it does. Took me to click on 4 different videos and maybe 20mins of watching in total to get to this one
Prob that visitor lands before 6:01 and before 6:21 are the same due to memorylessness. When applying the same logic to the problem you solved last, I don't get the logic behind the probabilities differing. Those should also be the same using the same logic and memorylessness?
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.
This video really helped me a lot understanding the difference between Poisson and Exponential distributions. Outstanding ❤ Thank you and keep up the good work 🙏🏻
thank you sir, great explanations and really helpful 😅😅👌👍 though in between the moments i do notice certain use of of rough language, just an advise on what could make these better. Personally i really like the way Mr. Grant on 3B1B talks, utterly admiring the beauty of the subject.😅😊 (to be quite precise, the beauties of geometrical patterns in curves of graphs and sequences and series that make them look the way they do, shall never be compared to a can of worms in my opinion, i am sorry)
Hi, first, grangrats for this amazing channel. I've got a question. In timestamp 17:00? Shouldn't we say probability for the second hand side statement should be formulated as P(20
Oh great! FYI- People dying from Keto will perhaps follow a Poisson distribution 😀. And the reason will most likely be kidney failure and not rise in HbA1c
Not really, because the X axis is continuous, rather than showing discrete values. 30 minutes is a moment in time on the X axis, with zero width. So the probability of the next visitor arriving at exactly 30 minutes is 0. So 'P(X
in section 4, where you calculate F(x) ie CDf, it should have an integral formula, correct? for within 10 minutes, it would be integral from zero to 10 where that integral evaluated at t=0 is zero [1-e^0] and at t=10 the pdf f(x) is 1-e^(-x/u) is 0.39. but not sure where the integral is rules are being applied - meaning, integral of x is x^2/2 so what would be integral of 1-e^(-x/u) and then that integrals answer should be evaluated at t=0 and t=10.
This channel is underrated.
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.
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 website!!!!! Thanks a lot!
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!
Thanks edu boss! Share it round! :)
The best intuitive video on exponential distribution I have seen so far.. Thanks Justin for sharing.
Best I've seen by far
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.
your voice so soothing bruh, it plug all the theories into my head perfectly
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!
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!
the last few minutes gave the most important intuition! Thanks! 17:05 Why is it called "Exponential"??
Because 0.95 keeps getting multiplied by itself in the function. In other words, it is a constant being raised to a power, which is the nature of an exponential function.
Would have been nice to state that the y-axis on the exponential dist is lambda for the PDF and a percentage for the CDF.
Unlike the Poisson Dist as both are in percentage.
This confused me as I wasn't sure what the Y axis meant. I naturally thought percentage and was wondering why nothing was adding up correctly especially at 16:44 - I was like, it should equal 0.025 or 2.5% which is of course wrong. I watched the whole video with the wrong assumption haha
It's mentioned on the y axis, the values. So it's kinda self explanatory 😅
you are right my friend. I had the same doubt throughout the video
- The Y axis on the exponential distribution PDF does not represent Lambda (nor the probability). It actually 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. But you're right that this was not explained at all in the video.
- The Y axis on the exponential CDF and the Poisson distributions is probability, on a scale of 0 to 1, and not percentage, which would have a scale of 0 to 100.
I swear bro you are one of the best teachers out there!
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 :)
Brilliant teacher , very clear with a commonsense approach.
Clearest stats video I have ever watched. Thank you
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.
All I can say is Thank you from the bottom of my heart.... This saved me...
Thank you just soooo much! May the lord give you paradise in this in this one and afterlife.
The last problem was just a fantastic one. First you treat it as an exponential distribution, so the probability of within one min becomes your probability of success. Then you treat it as geometric distribution. Brilliant!
Wow. Just wow. This video is marvellous! We really appreciate your effort!
Brilliant, loved the simple PDF explanation at the end
Best content for learning statistics for data science
These videos are incredibly informative ! I encourage you make some more !!!
Best intuitive explanation I’ve found. Thanks!
The way you explained why the pdf looks like it is really amazing! Thank you! I finally realized exponential is related to binomial distribution!
pois(X) and exp(X) bless you sir for this great lecture. Wonderful.
Awesome. Especially, the last sections explanation was crystal clear. Thank you.
Awesome explanation, Sir
Best channel for Statistics!!!
This is a kind request to have a video series on Permutation, Combination ,Probability and Calculas. I must say your videos are very awesome. The way you explained things is fantastic. Thanks Justin
Omg, cant believe this video doesnt have more likes! top level sta video!
This video is amazing the only video which explains exponential distribution in depth . Thankyou so much
Great explanation. Cannot be better than that. Crystal clear my concept. Thanks
Man i would have never understood it any other way. Outstanding explanation 👏👏👏
Thanks for the wonderful explanation. Just one confusion in the section "Visualisation (PDF and CDF)" - the Exponential distribution graph at @6:35 minutes is correct? because on the Y-axis you have put values greater than 1. but shouldn't these values be less than 1 representing the probability?
amazing videos. your explanations, oration, recording, and visuals all are superb!
This really helps me understand how the statistical tests built on these distribution works!
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.
Thank you Nick! ❤
@@rom3o.s_regr3t You are welcome, Bontle :)
The best video for understanding exp dist...loved the way it explains!
Amazing Class! Salute from Brazil.
Appreciating your smart way to lead us through exponential distribution
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🙏🙏🙏🙏🙏
I understand how simple it is just because of your this video. Thank you so much.
wow! really good explaination
Saving lives. My lecturer and textbook use lambda as both the Poisson mean and Exponential mean. Can't begin to explain how many hours I wasted not realising they were referring to two different means. Thought I was losing it. Was ready to drop out of math and try my luck in humanities.
Thank You so much for the explanation in the "exactly" scenario, zedstatistics. This helped me a lot. Thanks a million.
TH-cam algorithms must be pretty good that it didn’t take me long to find this video on exponential distribution >< This one answered my question exactly which is why the exponential pdf looks like the way it does. Took me to click on 4 different videos and maybe 20mins of watching in total to get to this one
Prob that visitor lands before 6:01 and before 6:21 are the same due to memorylessness. When applying the same logic to the problem you solved last, I don't get the logic behind the probabilities differing. Those should also be the same using the same logic and memorylessness?
Best explanations ever. Thanks.
you re video is just perfect. you also explain very well why things are like this or like that
You are so good in explaining maths.
You are an incredible instructor.
Great video thanks for the help!
Thank u so much!These lectures are very intutive!!
I think one of the best explanations on Exponential Distribution. Could you please share any content with its link to CTMC and Transient Analysis.
Did I just learn what exponential distribution is? :)
Thank you!
Ohh man you made me very clear on exponential distribution thank you so much for it . Also please make a video on Gamma distribution
@7:36 what is the unit on the Y-axis of the graph to the right?
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.
Wow this is soo coool! It is a great addition to "Practical statistics for data scientists" book. Thanks!
Fantastic video. Keep it up.
This video really helped me a lot understanding the difference between Poisson and Exponential distributions. Outstanding ❤ Thank you and keep up the good work 🙏🏻
very very clear explanation. Thank so much. You did help me to understand Possion and Exponential!
Simply superb, thanks for making these videos. Hope you keep making more videos on statistics!
This topic was explained very nicely. Thank you.
archangel of stats explanations thx zed
After seeking around a lot of videos its the only video which shows why its PDF looks the way it looks
thank you sir, great explanations and really helpful 😅😅👌👍
though in between the moments i do notice certain use of of rough language, just an advise on what could make these better. Personally i really like the way Mr. Grant on 3B1B talks, utterly admiring the beauty of the subject.😅😊
(to be quite precise, the beauties of geometrical patterns in curves of graphs and sequences and series that make them look the way they do, shall never be compared to a can of worms in my opinion, i am sorry)
3:00 The horse kick deaths were decreasing by the same ratio as soldiers got run over by cars.
Interesting. when you were explaining the pdf, I couldn't help but notice that behavior was similar to the geometric distribution. I wonder why.
Fantastic explanation.
Hi, first, grangrats for this amazing channel. I've got a question. In timestamp 17:00? Shouldn't we say probability for the second hand side statement should be formulated as P(20
Did you find the answer to the question? I have the same doubt
Oh great! FYI- People dying from Keto will perhaps follow a Poisson distribution 😀. And the reason will most likely be kidney failure and not rise in HbA1c
what's the answer?
He's the teacher we never had.
so cool, I wondered why distribution looks like that. so clear now!
Damn that's awesome! Now i understand where the ' exponential' came from.🎉
Okay, okay, so anyone would listen to Justin explain even how sand is made. Thanks for the video !
Sand videos, hey? That's really gonna take my channel in a different direction but let's do it!
This was really helpful! Thanks a lot for your kind effort.
Thank you so much. This was very well explained.
Great explanation man !!!
Fantastic. Keep up your good work!
Thanks a lot. That really is an awesome explanation
Amazing explanation
14:35 4th line
since it is cdf, wouldnt it be P(X
Not really, because the X axis is continuous, rather than showing discrete values. 30 minutes is a moment in time on the X axis, with zero width. So the probability of the next visitor arriving at exactly 30 minutes is 0. So 'P(X
The last part reminds me of the binomial distribution without de combinations in the formula.
I cannot thank you enough for this video
your explanations are really great. could you do more distrubution videos
Great bro. Great 😊😊👏👏
thank you so much for the explanation on exponential distribution i found it easy to understand
Thankyouuuu so much!❤❤, Very well explained
Great explanation! Thank you very much
Thanks so much! Great video and helpful visuals!
I always thumps up before watching you're videos :p
Hello Sir, I have watched many of your vedios..And I really like those.. Kindly make one vedio on endowgenity. or suggest me some source.
Thank you.🙂
Sir, thank you so much for the very clear lesson :)
Great class!
Very good video. Thank you.
Great work!
You saved my life.
Thank you! So easy and clear ❤️🙏🏻
in section 4, where you calculate F(x) ie CDf, it should have an integral formula, correct? for within 10 minutes, it would be integral from zero to 10 where that integral evaluated at t=0 is zero [1-e^0] and at t=10 the pdf f(x) is 1-e^(-x/u) is 0.39. but not sure where the integral is rules are being applied - meaning, integral of x is x^2/2 so what would be integral of 1-e^(-x/u) and then that integrals answer should be evaluated at t=0 and t=10.
At 18:18 i dont' think the probability is the same -should be formulated as P(20