An Introduction to the Poisson Distribution
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- Опубликовано: 30 сен 2024
- An introduction to the Poisson distribution. I discuss the conditions required for a random variable to have a Poisson distribution. work through a simple calculation example, and briefly discuss the relationship between the binomial distribution and the Poisson distributions.
Plutonium-239 example (an average of 2.3 radioactive decays per second).
Finding the probability of exactly 3 radioactive decays in a 2 second period:
dpois(3,2*2.3)
[1] 0.1630676
Finding the probability of no more than 3 radioactive decays in a 2 second period:
dpois(0,2*2.3)+dpois(1,2*2.3)+dpois(2,2*2.3)+dpois(3,2*2.3)
[1] 0.3257063
or
ppois(3,2*2.3)
[1] 0.3257063
WARNING: Watching many jbstatistics videos may cause you to actually like probability and statistics!
Dude, you make the best stats videos. My textbook is horribly written, and your videos along with the lectures are very helpful. Continue to make this videos!
This video helped me understand Statistics and Probability in 9 minutes better than my teacher did in 2 hours a day
Thanks for sharing this valuable lesson. See you again!
Wonderful explanation, thank you!
Very helpful!!!!
Cool vid
At my graduation I'd like to thank RUclips for teaching me all that I need to know to pass material in school. Thanks bud.
I didn't have RUclips 20 years ago, it was much harderback then. I m relearning this from scratch.
I didn’t have these RUclips tutorials in high school and I really wish I had these tutorials. Traditional study materials don’t have the changing visuals that videos do. Glad you were able to make use of these videos!
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Have you graduated yet?
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So much easier to follow a youtube video at your own pace, instead of a lecture at 8 am.
It also helps that the video is just great anyway ;)
+King of Dongles I'm not too keen on 8 am lectures either :) I'm glad you found the video helpful!
Your videos are extremely helpful.
THIS
Thank you,, surely you are helping me
@@jbstatistics awesome work...
Every time you say "Poisson" I think of carl saying croissant
damnit now i cant unhear this lol
Just think about the Poisson Distribution of croissants finished in a day.
ruclips.net/video/dg2S08WAIAo/видео.html You love to see it
Reminds me of Tom Holland too lmao
these video's are life savers when your stats professor has no idea how to actually teach properly. Seriously my stats professor just puts random stuff up and gives examples, but doesn't explain how to actually do them
Yeah you are right ..
SAME HERE
Omg same🤦
Its been like this for years. They write the equations but never elucidate or describe how significant each term in that equation really is. I'm guessing professors never give a single fuck about what the students learn. Now thats not all that bad but hell, classes are a waste of time. Even more so, when the professor insists you attend them regularly. The time that I've lost attending useless classes will never be made up
👍👍👍 m.ruclips.net/user/djganit
Exceptional videos for review just before the exam. Thanks a million.
Shaun Roberts You are very welcome!
Maybe as a little motivation for you to continue this great work, I had to do a statistics test and if i didn‘t get a sufficient grade I would have been kicked out of my programme because I didn‘t have enough credits. I just made it. If I didn‘t see this video I would not have understood poisson in such short time and it was a significant chunk of the test. Thank you very much.
+Lemarocity You're very welcome. All the best in your future courses!
All you had to do is actually start studying when it was taught weeks if not months before the test.
The video is amazing nonetheless.
I literally should be awarded a Bachelor degree from university of RUclips, rather than my actual university
all this time i thought it was pronounced as "poison"
I watched this and said Poisson after every time you said it. 10/10 video, thanks!
That's a good idea --- it's a fun word!
Dude, you're THE DUDE OF STATS
Such polished content! Many Hours of hard work must have been put into this. Greatly appreciated!
I have a statistics exam on Thursday and I FINALLY feel like I understand this. Thank you so so much for these videos! :)
You are very welcome! I hope your exam went well!
great video. Better than my Lecturer.
You're welcome Jakob. I have a video where I derive the mean and the variance of the Poisson distribution (ruclips.net/video/65n_v92JZeE/видео.html) and a video where I show that the binomial distribution tends toward the Poisson as n tends to infinfity, and lambda = np stays constant (ruclips.net/video/ceOwlHnVCqo/видео.html). Cheers.
You hit the sweet spot between quick and simple and slow and relaxing. Even after I'm done with my exams, I'll surely come by every now and then for some relaxation therapy. Your voice is so soothing. ^_^
Thanks! I don't tend to get too many people coming back after their course is done. I look forward to having you as a viewer for many years to come :)
jbstatistics
Hehe. Sure ;)
Sometimes it's just nice to learn some cool math stuff.
He's like a more detailed version of 3blue1brown
THANK YOU SO MUCH YOUR VIDEOS HAVE HELPED ME UNDERSTAND STATS MORE THAN MY LECTURER WHO MAKES ME FALL ASLEEP BAHAHA
THANK YOU!
Can we say that Poisson distribution is a discrete function?
I'm currently taking an online course and it's turning out to be much harder than I thought it would be. Thank you for having these videos that are so detailed.
I wonder what your doing with your life now?
Deep thinking
I just wanted to say thank you for your excellent work :D
Your videos and explanations are so incredibly clear. I love watching them even as a review just because of how well you explain things.
You just saved me from my midterm. Thank you so much!!
Thanks for the correct pronunciation, bit of a pet peeve when people don't silence the n
This is well explained. Thanks so much.
You are very welcome!
Worked example, consistent with the notation and clearly spoken. Excellent tutorial
Just changed my degree to Actuarial Sciences. Brushing up on my stats in a much more thorough way than my horrible stats classes ever covered the content. I'm trying to use my free time this summer to take detailed notes on all of your videos and many other Statistics relevant RUclips channels. Thanks for the concise yet intuitive content!
You are very welcome!
Thanks sir🥺your video really helped me😍
leave the thumb up first, then go over the lecture! This is my habit for this channel!
The probability that an event occurs in a given length of time does not change through time-Does that mean the number of accidents occurring in the first 1st hour would be equal to number of accidents happening in the consecutive hour?
Quick question, I tried the equation on my calculator, but it's giving me 0.8076790144
The... the production and information value of this video... THANK YOU SO MUCH, FELLOW HUMAN.
i still dont get what poisson distribution is......i guess i can now calculate it, but have no idea what it means.
Perhaps watch this video carefully again, or try this other one of mine:
Poisson or Not? (When does a random variable have a Poisson distribution?) ruclips.net/video/sv_KXSiorFk/видео.html
Thank you for this video....easy to understand 🙏
I'm glad to be of help!
Great explanation mate! Thanks to people like you, we are able to score well in exams!
Very helpful, thank you.
Such a clear and beautiful explanation. Thank you
much much more succinct and helpful than an actual school lecture. thank you
Thanks to you, thanks to @youtube 😊
You Sir have my salute!
Yea but it is discrete, what about continuous Poisson distribution?
It's right next to the discrete normal.
Heh, learning everything the night before the exam checckkkkkkkkk
yes
but...how DO we work it out on a calculator? This is stumping me hardcore; this part is overlooked 😞.
EDIT: if anyone else is struggling with the inputting into calculator I recommend these 2 vids
ruclips.net/video/ovXnjiubdWs/видео.html
ruclips.net/video/I9LIvbXSsQc/видео.html
nobody:
nobody at all:
poisson distribution: PLUTONIUM-239 IS AN ISOTOPE OF PLUTONIUM THAT IS USED IN NUCLEAR WEAPONS AND REACTORS
Sometimes, I feel like I have a very large end and a very small pee 😞
ASSALAM U ALLIAKUM
sir you made excellent videos of all the topics and plz make videos of all remaining videos like
fourier series
many others thanks
Thanks for the kind words, and I'm glad to be of help! I'll get back to video production soon!
how come its 2.3 x 2 and not 2.3 x 3? and how come its multiplay not add? I always have trouble knowing which numbers to use.
Wanted to start a career in Data Science. I think this channel has many statistical lectures explained in a succinct manner. I don't wanna miss a lecture. That's why I subscribed it. Thank you very much for your videos
You are very welcome! Thanks for the kind words.
For real you tube has contributed almost 80% to my understanding of calculated course unit's.
Thank you. Im really a fan of poisson distribution
I have 2hours to understand, solve, and answer my hw that ive been trying to understand for the past 4hours. (Might update later)
When n is large and np is bigger than we approximate the binomial distribution to be a rough normal distribution. So, when n is large, p is small, and np is bigger than 10, the distribution both approaches to normal and poisson distribution ?
Thanks Easily understood in 5 mins even while cannot understand during 1hr lecture 😅
Could you explain why poison can’t take negative probabilities?
Thank you very much for all your explanations, they are great!
alexandra-stefania moloiu You are very welcome!
What do we mean by radioactive decays per second? Does it mean that 2.3 atoms will decay each second?
Thanks you sir
For sacrificing 4 us wz this perfect teachings
Why did you take Lemda as 4.6? While you said Lemda is mean. Can you explain this?
how to identify which method(binomial, bernoulli , poisson )to use in a question
At our uni our maths lecturer pronounced this as poison distribution and now I learned it's po-sson f
better than khan academy about statistic.
Agreed :)
Hello! Thanks for uploading the video! Ur explanation is great! By the way, is it possible for you to explain MORE? For example, the derivation of some formula? Derivation of the Probability Mass Function? Derivation of Mean and Variance? :D
Aren't all models merely an approximation of the underlying reality?
i think i need to go back to digging holes. I was lost after the first 2 minutes
I don't understand why lambda is doubled in the first example and then plugged into the formula or more precisely why we are allowed to do this trick (I'd like to see some calculations, precise mathematical reasoning.). Why don't we leave the lambda as 2.3 and instead add probabilities of Poisson process for first second and then second second with lambda=2.3 so that we get 3 radioactive decays within two seconds p1(X=0)*p2(X=3)+p1(X=1)*p2(X=2)+p1(X=2)*p2(X=1)+p1(X=3)p2(X=0)?
It's not a trick. Lambda represents the mean number of occurrences in the time period under discussion. For a 1 second period, the mean is 2.3. For a two second period, the mean is 4.6. Your way would work as well, but it's a bigger hassle to carry out that calculation.
The sum of independent Poisson random variables is also a Poisson random variable, with mean equal to the sum of the individual means. The easiest way to show this is through the moment generating function technique. That's often covered in a first course in mathematical statistics, but not typically shown in intro stats, and requires too much background for me to show in this box.
these videos are golden, thank you so much!
You are very welcome. I'm glad you find my videos helpful!
why can't teachers at University explain like this? Clear, simple and putting sense to the formulas, not just throwing it at your face without context. Grr
Thanks!
You are very welcome. There are many, many good teachers at universities. Different students have different learning styles and abilities, and it's difficult to determine the best level at which to pitch the material. I'm sure some of my own students don't like the way I approach certain things. It also depends on the course. In a more mathematical course, I would approach this topic very differently.
That said, I do try to give illustrative examples wherever I can. Tossing up a formula without context and examples is not usually a great approach.
I'm glad you found this video helpful, and thanks for the compliment! Cheers.
I want to record your voice saying Poisson and use it on a rap song XD
What a brilliant talent for teaching you have, thank you
this is really understandable thank you!
Hi. Why is P(k) equal o P(k-1) , k=lambda, for the Poisson distribution?
Example: for Poisson(lambda=3), P(2) and P(3) are both equal to 0.2240418
how do you input e into the calculator?
thank you sir, really well explained and helpful.
At my graduation I would like to thank RUclips for teaching me all the possible ways of simplifying things😂
samehere😅
8:25 what videos explores the relationship between poissino and binomial in greater detail?
My video outlining the relationship between the Poisson and binomial distributions is available at ruclips.net/video/eexQyHj6hEA/видео.html.
You said what is e but you didn't say that what is the reason of using e???
Bro, u know what, u are amazing!
well i went from indisputable dumbass in stats to slightly less of a dumbass, just in time for my midterm
thanks again dude, appreciate your efforts in making such a helpful video
Do u do statistics ?
So the poisson process is basically the poisson distribution. In poisson distribution we have time when we define lambda, and in poisson process we have time outside the definiton of lamba (lamba*t=mu(t)) ?
Easy to understand, even for not so brilliant people like me :D, and beautifully explained. THANKS!!!
Hey! don't read the comment, focus on the video!
really awsome1 great job! keep goinh
One Question .. Why did the graph consider one second interval, while the mean is for 2 seconds. i mean the mean was 2.3 seconds it is 4.6 for 2 seconds
I don't know what you're asking. The plot represents the probability distribution of the number of decays in randomly selected two-second period.
Such an easy and clear explanation, I just love it.
And here I am, getting prepared for an 8AM lecture on probability. Final Exam in 12 hrs. XD
Hi! Can you help on analyzing the statistics on shoplifting and getting the probability that an event of shoplifting may occur. tnx
Please check.. the next video in this playlist or 7th is private. I can't view it :(
What happens if the second Poisson isn’t true?
I can’t expect that customers come in at the same rate at 8am-9am vs 8pm-9pm
Is it stochastic?
Nice explanation, but don't say a "length of time" but "interval of time".
That wouldn't work. The total length of the interval or intervals is what matters. Had I replaced "length of time" with "interval of time" the meaning would be lost, and the statements I gave would not be true.
Thank you for your amazing explanations. Much better than my boring statistics teacher.
I love watching your videos, it helps me a lot. since, it way easier to understand that my teacher, lol.
Thank you so much. Now I can feel relaxed and have a tight sleep with this thing. I love you hic
I really enjoy your content mainly because of how clear and concise you are, also your voice is almost relaxing.
great that you showed "no more than 3" solution,, but what if we needed to find the "''more than 3''?
Subbed because you are the man. I will comment this on all the videos of yours that I will see.