An Introduction to the Binomial Distribution
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- Опубликовано: 1 окт 2024
- An introduction to the binomial distribution. I discuss the conditions required for a random variable to have a binomial distribution, discuss the binomial probability mass function and the mean and variance, and look at two examples involving probability calculations.
The estimated probability of a 90 year old Canadian male surviving for one year was taken from Statistics Canada life tables, which can be found at www.statcan.gc..... The probability given in the table is the estimated probability that a randomly selected Canadian male, given survival to his 90th birthday, survives until his 91st. I simplified this explanation a little in the example in the video.
For those using R, here is the R code to find the probabilities for the examples in this video:
Die roll example.
Finding the probability of getting exactly two fives in three rolls:
dbinom(2,3,1/6)
[1] 0.06944444
Twenty randomly sampled 90-year old Canadian males example.
Finding the probability that exactly 18 survive for at least a year:
dbinom(18,20,.82)
[1] 0.1729609
Finding the probability that at least 18 survive for at least a year:
dbinom(18,20,.82)+dbinom(19,20,.82)+dbinom(20,20,.82)
[1] 0.2747932
or
1-pbinom(17,20,.82)
[1] 0.2747932
where Khan Academy failed you my friend helped loads
I'm glad to hear it helped! Cheers.
Tycho Thorpe me also bro.khan academy 🤕🤕🤕
@@surujdeka8544 I also just came from a Khan academy to this one
@@monalisanokhemane3099 So true
@@monalisanokhemane3099 Hahaha, wow! I really thought I was the only one like that. Felt dumb to not understand even Khan academy video because they teach school level stuff, but this video did much much better than KA :)
How the heck am I finding this channel only in 2019? This is a gem of a channel!
Thanks!
Your videos are very helpful. Also your voice is pleasant.
+CrystalData Thanks!
Hi JB,
I was wondering if you could tell me why count the probability of failure too? For example, most questions ask for the probability of success but for some reason we count the failure too? Why is that?
Because you are calculating the probability of X=x, or that x is equal to exactly something. By leaving off the probability of failure, then you are essentially saying the third roll doesn't matter, it can be a success or failure. For example, in the die problem, we were looking for exactly two 5s. However, if you calculate just the probability of two successes and leave off the third roll, then you get 0.083. Now, notice that if you calculate the probability of exactly two successes and a failure you get 0.069, and if you calculate the probability of exactly three successes then you get 0.014. Adding these together you get 0.083. Therefore, if we are looking for exactly two successes and one failure, then we need to add the probability of the failure in, which in the case of the die example, gives us 0.069.
The best is when you watch it on 2x speed
Flirting in the classroom *wink* *wink*
You are a fucking savior.
Meanwhile my textbook is speaking to me in a foreign language.
Thank you so much!
Extremely well explained, very clear and very logical presentation. It is one of the best educational videos I've seen. Thank you!
You just saved my degree thanks
ill wait till i see my mark to say the same
@@opq3264 and how?
м Владислав My final is next week , but let me tell it’s not looking good at All for me 🤦♂️
Are you rich now?
@@viktorbranco8362 haha :D
Hi. Thanks for the feedback. Most of my videos move at a fairly quick pace, but some are a little bit slower. I take a bit of a different approach than many others, and moving things along at a decent clip is part of that approach. My pace in this particular video is just a smidgen faster than I'm aiming for. I imagine that at some point in the not-too-distant future, we'll have full control over playback speed so it will be easy to adjust that to one's own tastes. Cheers.
your prediction was right!
Prophet
Spot on, sir!
And many thanks for the great tutorial !
genuinely your explanation are bit fast but they are very precise and very good ,thanks for helping so many and ofcourse me.
He saw the future
Excellent Video :) Truely , you are the best teacher.
Mans a legend.
I missed 3 lectures due to work and an illness. Thank you very much for making such wonderful videos illustrating these topics.
+Justin Robertson You are very welcome Justin. I'm glad you've found them helpful!
Thanks a lot! You saved my grade!! My professor and textbook are horrible
These videos are SO good. They should be supplemental material for all intro uni stats courses
Thanks for the very kind words!
You're quite articulate, JB. The visualizations really help. It helps that you do several examples from different angles for each problem. Thanks for connecting the dots!
You are very welcome!
This gave so much clarity amidst the confusion I had on this subject. You made it seem so simple. Thank you.
I'm glad to be of help!
Seriously some of the highest quality math lessons I've come across!
Thanks!
I do not have a mathematical background but find your videos are clear and helpful. I struggled with solving the equation. Would you please explain how you arrived at 0.173 from the 1st line? 0.82^18 = 0.0281; (1-0.82)^2 = 0.0324; 0.0281 x 0.0324 = 0.0009. I am missing something.
You forgot the (n k): 20!/18! --> (20*19*18!)/(2*1*18!) = (20*19)/(2*1) = 10*19 = 190. Now, 190*0.0281*0.0324=0.173
Thank you very much this was so helpful 😃✔️✔️
My professor does not explain this NEARLY as good as you. Everything I learned in class felt like a jumbled mess. You took all of that and made it crystal clear. Thank you so much.
exactly
You guys have one where you pretend to explain this to a five year old? I might need that one.
amazing teacher, you made my statistics class go by smoothly. Thank you.
Absolutely smashing video.
Thanks!
This was very helpful, thank you
Love your work! Thank you so much for educating me.
Hye Dien 💓
I have just posted how to find probability using Binomial Distribution..... I hope it's helpful....
Watching this video in 2020 , still can't believe you deliver this quality content 7 years back .
Truely Amazing.
6:42 Bro ,can you tell me why he is forming a tree like that? I can't understand the tree structure.
this is so great. this is the third video I watch in a row because those topics are part of 1 chapter that I have on my Midterm on Saturday. and you're covering them quite nicely !! :)
It's like you're doing exactly what my teacher wants me to learn for my exam! haha
Thanks so much . That tree diagram is very helpful.
Hello John💓
I have just posted how to find probability using Binomial Distribution..... I hope it's helpful....
How do you punch in everything on your calculator sir 😭😭
I keep finding different answers
hidden gem of youtube
Indeed :)
please can anyone explain how he calculated the answer to be 0.173, 0.083, 0.019. please i am getting confused with the calculation. i think the lecturer calculation is wrong compare to my own interpretatin
me too
I'm from Spain, and I always see your videos when I need help because the way you explain the lesson is awesome and your pronunciation helps me a lot. Thank you so much!!!
+Ana Villanúa You are welcome Ana! I'm very glad to be of help!
You are very welcome Ahmed. I'm glad to hear my video helped!
I was failing A level maths and this helped so so so much, thank you so much
im so sad that i found this channel a day before my statistics final
Better to find the good stuff a little late than not at all. I hope your final goes well!
thanks for saving me
Your videos are the best!!! Seriously, thanks for saving my stats grade!!
+canucklehead You're very welcome! Thanks for the compliment!
How to multiply the (20 and 18) to the other equation. Will you be able to show the work as well in your future videos. How you arrived to the number 0.173.
I'm watching this after a long day at 6 am and it STILL makes sense. That's how good this video is.
Hello I have a question please what dose the number 0.173 mean in English? Is it 17% of 18 men will stay stay suivre ? Means only 3 men out of 18 men will stay alive for the next year ? Thanks
Dude is an amazing instructor and secretly funny af. thanks for saving my grade!
I have just posted how to find probability using Binomial Distribution..... I hope it's helpful....
you deserve more subs, god bless u
This is very good explanation, but at 5:48 this ans is incorrect. n/x must changed to Nfacorial by Rfactorial - nfacorial-xfactorial.
Well Done
Thast really Gem droping such knowledge
Thanks Sir
I can't think of a better explanation than yours.
Great video man, really helpful !!
I feel like skipping the rest of my 55min lectures, which I don't understand at all, and just watch your videos. It would be much more efficient.
Thanks again!
That attendance policy
I love having equations explained to me in a way I understand. Thank you
9:05
Your voice sounds like Jarred Dunn, from Silicon Valley!
in R, P[X = x] = dbinom(x, trials, probability).
well, it seems that youtube is the future of learning
the quality of these videos is way higher than college lectures
Subbed, because you are the man.
Thank you So Much.
i can't like this video enough(usually i dont comment very much but this thing i could not understand and you explained it very well!! may Allah bless you!!!)
Happy to be of help! Thanks for the kind wishes :)
Sir thank you for your quality lessons, in example of, "According to statistics Canada......." where was n=20 derived from?
In the problem I stated "If twenty 90-year old Canadian males are randomly selected..."
at 1:19 if independent, why is it like pIIx = p ^ x , that is read as (p pi x) this statistics comes from the fact as to when the balls are distinguishable and replacement is possible for trials.
even when the balls are indistinguishable, but the binomial statistics treats the balls indistinguishable... this is what i MUST know.
wish to fundamentally derive the binom distribution from (number of outcomes you want) / (total number of trials). what would be the total number of trials here for a starter?
I genuinely do not know what you are asking. For example, I could only guess as to the intended meaning of this:
"even when the balls are indistinguishable, but the binomial statistics treats the balls indistinguishable... this is what i MUST know."
First, we have to speak the same language. In the binomial there are n trials. That's the number of trials. But that's not what you mean by trials in your last sentence.
Also, not all probabilities boil down to (# of outcomes that result in the event)/(Total # of outcomes). That's only true when the outcomes are equally likely.
I like your fast version explanations better because they are sassier.
Love you, thanks dude. You are auxiliary for me.
Bravo! Your explanation is very clear and helpful! Excellent!
Thank you! I'm glad to be of help.
Legendary video
Thanks!
Watching these videos in 2022 🤟🏽
They're still the best :)
@@jbstatistics it really helps me, hopefully my test will be fine tomorrow
Sir!!! I salute you!!! Thanks a lot for your lectures. I am enjoying your lectures. i was so scared of probability. THANKS A LOT SIR!!! GOD BLESS YOU. i was almost at the verge to drop this class, and your lectures has just showed me some hope.
You are very welcome Usman! I'm very glad you've found my videos helpful. All the best.
Sorted out all my problems - thank you
this explanation was so good!! thank you so so much
Once again thank you. My instructor teaches in the same manner that you do and with these videos to reinforce everything it gives me the supplemental instruction I need. I am going to subscribe to this channel and use these videos to help study for my tests.
You are very welcome Tracy. I hope you find my videos very helpful!
Man, seriously, as an educator myself I can tell
you are outstandingly good at this.
i need help i dont get howhe got 0.173 at 11 mins
sorry how is it 0.173? i keep getting 0.001???
6:05 - that was the key revelation to me about the formula!!!
Thanks a ton. Great help in getting the basic understanding right
gouthamsandeep reddy You are very welcome. I'm glad to be of help!
jbstatistics A great help. Love your clear accent and understandable examples. Thanks a lot. im sharing it with my course mates.
Anas Bin Harharah You are very welcome!
Suppose Y follows a binomial distribution with n=2 and p=1/2. Find F(y)
2Cr * (0.5)^r * (1-0.5)^(n-r)
Sensational stuff
I try to calculate the toss coin and the CANADIAN ...
the toss coins equals to "0.0833 and not 0.0694" X.x WHY???
AND FOR CANADIAN
"its 20.6809 not 0.173" WHY?? I TRY CALCULATING IT 3TIMES BUT ITS THE SAME ANSWER ??? O.O???
FEED BACK PLEASE ~< T.T
I don't know where your numbers are coming from. (It's not obvious to me what your calculation error is.)
I think the 90 year old men who want to live another year would be very worried about that serial killer however.
Great video though, helped out a lot.
I'm glad you found the video helpful! (I wasn't saying that we don't care about 90 year old men dying, just that the serial killer scenario was a little far fetched and probably something we needn't worry about :)
I wish I learned probability in this way earlier.
This is sooo helpful. Thank you so much!
Thank you
Hye David Chong💓
I have just posted how to find probability using Binomial Distribution..... I hope it's helpful....
Do you need to use your calculator to solve (n choose x)
please how did he finalize the result to be 0.173.pls can anyone simplify the calculation for me please.Read the question from according to statistics canada life tables. i would be highly anticipating for the kind and loving person
I'm getting 9.1x10^-4 ???
well...video is fantastic, but only thing i didnt get is in Canadian problem...the probability of any 90 year ppl is 0.82,so if we select exactly 18 out of 20 the probablility is 0.173,i suppose it shuld be much higher than tat
Thanks for the compliment! The probability that exactly 18 out of 20 survive for at least a year is indeed 0.173. If this doesn't feel correct to you, consider the fact that there are many other counts that are quite likely as well, e.g. P(X=15) = 0.149, P(X=16) = 0.213, P(X=17) = 0.228, P(X=19) = 0.083 (as illustrated in the probability histogram).
oaky...got it
Bro, you are saving my life :) Thanks for your uploading in 2013.
In around 14 minutes you made the binomial distribution crystal clear, whereas my lecturer couldn't do it using 120. My hat stays off around you sir.
This video was very helpful to understand binomial distributions in probability💃
Mans out here doin God's work
Thank you sm for the crystal clear guidance
i am a student of applied statistics & guess what my probability teacher sucks . thank u JB for making this easy to understand
Brilliant video, helped me a lot! But I have a question: shouldn't the probability mass be the highest on the value, which is closest to the mean (16 in this case and not 17) or is such an assumption illogical?
In other words, is there any intuition as to why 17 at 11:20 is more probable than 16?
thanks thanks thanks thanks thanks thanks thanks thanks thanks thanks thanks thanks thanks thanks thanks.
You are very welcome!
such an amazing explanation.thank you very much ,,,,,
sorry, didnt get anything
so in the table at 11:40 I didnt get that. For explaining further, is it says that 6 men to survive exactly has 0 probability??
Thank you and Grateful.
awesome video! thank you!
Brilliant ... phenomenal video
Wow, this explanation was immensely helpful. Thank you!!
Gold video love your channel plz keep doing that stuff.
The book didnt make any sense, but you did. Really helpful, thanks!
Now i can go to my exam =D thanks
+ahmed aboaldahab You're welcome! Best of luck on your exam.
Thankyou so much.. This has helped me a lot as statistics is not my favourite subject. Anyways, great video. Keep it up :)
this a really beautiful video
fantastic job! Thank you for putting together the video.
Hi, I found the videos very clear and useful. One small comment: you should slow down a little bit the pace at which you present. The explanation goes too fast and it's easy to get lost when trying to figure out what you say. Best!