An Introduction to Discrete Random Variables and Discrete Probability Distributions

An introduction to discrete random variables and discrete probability distributions. A few examples of discrete and continuous random variables are discussed.
This is an updated and revised version of an earlier video. Those looking for my original Intro to Discrete Random Variables video can find it at: • Introduction to Discre...

Пікірлер: 154

  • @danfoley1604
    @danfoley16049 жыл бұрын

    Wow this was one of the most clear and concise math/stats videos I have ever watched. Thank you so much.

  • @jbstatistics

    @jbstatistics

    9 жыл бұрын

    You are very welcome Daniel. Thanks for the compliment!

  • @anuradhadas8795
    @anuradhadas87955 жыл бұрын

    I started studying about data science and came here whenever I had to revisit my concepts in statistics. One of the best and concise

  • @sanjulakammammettu4308
    @sanjulakammammettu43087 жыл бұрын

    This is probably the best introduction to statistics I have watched on KZread. The concept is explained in a wonderfully simple and crisp manner, with great examples. The speed of delivering the concept was perfect and it is presented in such a clean and un-fussy manner! Thank you so much for your video series; it makes studying statistics so much easier!

  • @julienbonin
    @julienbonin4 жыл бұрын

    You can tell how well this guy understands this subject by how well he explains it. Brilliant!

  • @boisterousb7702
    @boisterousb77029 жыл бұрын

    I'm sure I speak for everyone here when I say these videos are amazing. You make complex concepts easy to understand. THANK YOU!

  • @jbstatistics

    @jbstatistics

    9 жыл бұрын

    You are very welcome. I'm glad to hear that you find my videos helpful, and thanks for the compliment!

  • @WilliamKinaan
    @WilliamKinaan9 жыл бұрын

    One of the best understandable videos about discrete probability distributions. Many thanks, I really appreciate it

  • @jbstatistics

    @jbstatistics

    9 жыл бұрын

    ***** You are very welcome!

  • @yusuffarah351
    @yusuffarah3514 жыл бұрын

    I took so many stat classes at some point even tutor others, but never come a cross some one who can clearly explain this counter intuitive subject. Indeed, knowing a subject and teaching others is too different things. Thank you sir for sharing your knowledge to the world. As some one who love to learn and teach others , I am very grateful to find your videos.

  • @sourabhpadaki4169
    @sourabhpadaki41694 жыл бұрын

    It couldn't be better than this, crystal clear. Thank you for the crystal clear explanation.

  • @leanxious
    @leanxious4 жыл бұрын

    Watching this video is the best way to refresh my knowledge on this topic. Thank you!

  • @Giedre1237
    @Giedre12375 жыл бұрын

    it's so funny I had a lot of professors during my math studies and none of them taught me statistics as good as you did. thanks :)

  • @rebekahfollingstad2362
    @rebekahfollingstad23629 жыл бұрын

    Your videos are currently saving my life in stats class - THANK YOU

  • @xis9508
    @xis95089 жыл бұрын

    Thank you for the great course. You have a talent of explaining.

  • @jbstatistics

    @jbstatistics

    9 жыл бұрын

    You are very welcome!

  • @atheer2718
    @atheer27185 жыл бұрын

    Your way of explaining is so perfect! Thank you so much

  • @AmolMY
    @AmolMY3 жыл бұрын

    i think all professors teaching probability should watch your lectures..i magically understood all concepts..just amazing

  • @Soundlesskitty
    @Soundlesskitty6 жыл бұрын

    You are seriously my savior, my knight in shining armor. The one true probability & statistics messiah. My professor has an extreme accent, and I can barely understand a word that comes out of his mouth. Your videos on discrete probability distributions are pretty much the only reason I aced my test on Friday. Truly, from the bottom of my heart, thank you.

  • @jbstatistics

    @jbstatistics

    6 жыл бұрын

    You are very welcome! Thanks so much for the very kind words. I'm very glad I could be of help.

  • @wakka13371
    @wakka133718 жыл бұрын

    Thanks so much for all your videos. You've been a big help for me in my Prob and Stats class!

  • @nedst3r
    @nedst3r6 жыл бұрын

    Your videos are the best. You have no idea how much help they have been.

  • @jbstatistics

    @jbstatistics

    6 жыл бұрын

    I'm glad to be of help!

  • @HangNguyen-vg6hv
    @HangNguyen-vg6hv4 жыл бұрын

    Thank you so much. It made me more clear with what I learned in my statistics classes. I will go through your other videos. Many thanks.

  • @clowheeler
    @clowheeler4 жыл бұрын

    My classmate showed me your channel. Thank you so much for the videos! Theyre so useful!

  • @ethanjiang7070
    @ethanjiang70704 жыл бұрын

    best video of statistics I have seen so far

  • @kaycee5747
    @kaycee57474 жыл бұрын

    I got a 95/100 on my last exam because of your explanations and I would like to say thank you for explaining all the concepts so well.

  • @guozhee1795
    @guozhee17958 жыл бұрын

    thank you so much. This video really helps me a lot. I really hope my professor can be like you.

  • @jbstatistics

    @jbstatistics

    8 жыл бұрын

    +Guoz Hee You are very welcome!

  • @harshalshinde227

    @harshalshinde227

    8 жыл бұрын

    +jbstatistics love! love! love!

  • @jeanie8448
    @jeanie8448 Жыл бұрын

    Really grateful for these videos, thank you!

  • @WholeNewLevel2018
    @WholeNewLevel20189 жыл бұрын

    My whole respect sir, it couldn't be more clear than that .... thanks so much for this piece of art. pleas keep up...

  • @vaibhavverma9151
    @vaibhavverma91515 жыл бұрын

    You're one of the best teachers I've come across in my entire life. What an explanation. Killed it. I mean I don't know how to thank you for making such amazing videos. Thanks alot! Tomorrow is my exam..and I couldn't have understood this entire thing in one whole week which you made me understand in couple of hours. ❤️❤️

  • @jbstatistics

    @jbstatistics

    5 жыл бұрын

    Thanks for the kind words! I hope your exam went very well!

  • @paulacosico
    @paulacosico9 жыл бұрын

    You are a cool teacher. I hope I become as good as you someday. You are very clear in explaining. Thanks! I need this for my exam this Saturday. :D

  • @areenaamir9237
    @areenaamir92372 жыл бұрын

    YOU ARE AWESOME! SO GLAD I FOUND YOUR CHANNEL!

  • @kavithap1883
    @kavithap18836 жыл бұрын

    Hello sir my great vanakkam to you.. am from chennai Tamil Nadu.. Ur videos Everything am always watching .. u r such a great person .. am more impressed Ur teaching sir..

  • @sivakumar-vn7ex

    @sivakumar-vn7ex

    3 жыл бұрын

    I am also from Tamil nadu bro ,seeing this comment after 3 years☺️

  • @wesleyguan6833
    @wesleyguan68335 жыл бұрын

    too sad only about 150K views, I think it deserves 1 million at least. thx for your explanation!

  • @GoodLuckForever-wi9kb
    @GoodLuckForever-wi9kb7 ай бұрын

    Best Of Luck Forever For Sharing Such a Deep Knowledge in such a simple way. Well Done Sir

  • @suheladesilva2933
    @suheladesilva293310 ай бұрын

    Very helpful explanation, thank you.

  • @jamd890
    @jamd8902 жыл бұрын

    You will go to heaven, for making this videos thanks!!!!!

  • @brokenramen
    @brokenramen3 жыл бұрын

    oh my goodness thank you SO much! you're a god send!

  • @eldestisland4520
    @eldestisland45207 жыл бұрын

    Thank you so much for making this video!

  • @jbstatistics

    @jbstatistics

    7 жыл бұрын

    You are very welcome!

  • @Puhazhenthi
    @Puhazhenthi11 ай бұрын

    Great Explanation ❤

  • @Manas__yadav
    @Manas__yadav7 жыл бұрын

    he is so good....thank you

  • @TheVk30
    @TheVk304 жыл бұрын

    dude. if i learned everything with this level of clarity...

  • @thiagomfdn
    @thiagomfdn4 жыл бұрын

    Thank you so much for this video!!!!

  • @abrahamhagos8185
    @abrahamhagos81856 жыл бұрын

    thank you!!! the videos are amazing!!!

  • @jbstatistics

    @jbstatistics

    6 жыл бұрын

    You are very welcome! Thanks for the very nice compliment!

  • @mrx42
    @mrx424 жыл бұрын

    Give a chair of statistics and probability at MIT to this man !

  • @alyssavaldez8400
    @alyssavaldez84009 жыл бұрын

    Great video! Thank you.

  • @pranshukukreti9217
    @pranshukukreti92172 жыл бұрын

    Beautiful Explanation. Thankyou for this

  • @jbstatistics

    @jbstatistics

    2 жыл бұрын

    You are very welcome!

  • @dishajain7696
    @dishajain76962 жыл бұрын

    perfect explaination !

  • @charlesamieldionisio9981
    @charlesamieldionisio99818 жыл бұрын

    Thank you very much! Very clear and concise :D

  • @jbstatistics

    @jbstatistics

    8 жыл бұрын

    +Amiel Dionisio You are very welcome Amiel!

  • @matthewoancea5753

    @matthewoancea5753

    8 жыл бұрын

    +jbstatistics you've only replied to the people praising you saying that you're an excellent teacher. But it was very unclear for and many others where the 0.6 figure came from and you've ignored all of them.

  • @jbstatistics

    @jbstatistics

    8 жыл бұрын

    +Matthew Oancea I often do take time to offer points of clarification on my videos, but I make no promises about answering every question that I'm asked. Writing a reply of "Thanks for the compliment!" takes perhaps 10 seconds, whereas replying to a request for clarification often takes some time. In the example you are referring to, it's stated that "Approximately 60% of full-term newborn babies develop jaundice." I then state that the probability a randomly selected full-term newborn develops jaundice is 0.6. So the 0.6 is, essentially, given in the question.

  • @jaichatla8655
    @jaichatla86556 жыл бұрын

    Really very effective explanation awesome

  • @jbstatistics

    @jbstatistics

    6 жыл бұрын

    Thanks for the kind words!

  • @MUHAMMADKHALID-yx7up
    @MUHAMMADKHALID-yx7up6 жыл бұрын

    thank's a lot for your effort's professor Jeremy Balka's

  • @alishasalcedo5933
    @alishasalcedo59338 жыл бұрын

    how did you get .4 when you multiplied .6

  • @categorille8330
    @categorille83305 жыл бұрын

    Thank you jb, very cool

  • @zalida100
    @zalida10010 жыл бұрын

    Great video - thanks v much

  • @jbstatistics

    @jbstatistics

    10 жыл бұрын

    You are very welcome!

  • @El94Rey
    @El94Rey9 жыл бұрын

    actually u r excellent i'm from Egypt and i did not find any difficulities to understand this lesson ^_^

  • @adityashikhar6143
    @adityashikhar61433 жыл бұрын

    Thanks sir. You are great

  • @gitgosc7075
    @gitgosc7075Ай бұрын

    best of the best !

  • @urtvplugg5603
    @urtvplugg56037 жыл бұрын

    Excellent!!!!

  • @mido5219
    @mido52197 жыл бұрын

    you're so awesome!

  • @jbstatistics

    @jbstatistics

    7 жыл бұрын

    Thanks!

  • @hummus_boss
    @hummus_boss3 жыл бұрын

    Dislikes for this video come from uni's professors

  • @TheExceptionalState
    @TheExceptionalState4 жыл бұрын

    Great set of videos. Thank you! Good karma coming your way (depending on the probability that it is real and you believe in it :))

  • @michellerayeonpark7142
    @michellerayeonpark71425 жыл бұрын

    The best lecture videos

  • @jbstatistics

    @jbstatistics

    5 жыл бұрын

    Thanks again!

  • @paroleschansons7841
    @paroleschansons78412 жыл бұрын

    Thank you so much

  • @vanglequy7844
    @vanglequy784410 жыл бұрын

    I have been checking out other online courses to brush up my statistics skills. So far I find your videos are the best because they are easy to understand and the content are also advanced enough to me. However, some times in your videos you mentioned something like "this will be discussed in another video", but it is not clear how to find that video, for example: showing binomial formula at 13:10. And in general, I would like to see your videos about how to constructs probability mass functions for all well-known distributions (i.e. normal, binomial, negative binomial, Poisson, etc.). I feel that they all can be build based on basic probability rules, but I haven't found reading or worked out myself. Two other very interesting aspects: How distributions are related and how one can argue that the data follows a particular distribution. Could you make some videos about these?

  • @vanglequy7844

    @vanglequy7844

    10 жыл бұрын

    An update: I went to your website: www.jbstatistics.com/ . Relationship of video is well structured there. So I may be able to tackle the first problem (looking for related videos), but still very much interested in other things: " I would like to see your videos about how to constructs probability mass functions for all well-known distributions (i.e. normal, binomial, negative binomial, Poisson, etc.). I feel that they all can be build based on basic probability rules, but I haven't found reading or worked out myself. Two other very interesting aspects: How distributions are related and how one can argue that the data follows a particular distribution."

  • @InLoveWithFunkyPanda
    @InLoveWithFunkyPanda9 жыл бұрын

    Love this~

  • @jbstatistics

    @jbstatistics

    9 жыл бұрын

    Thanks!

  • @vansikasingh3228
    @vansikasingh32283 жыл бұрын

    thank you so much!

  • @sivakumar-vn7ex
    @sivakumar-vn7ex3 жыл бұрын

    8:40 ,why are we having two 0.24s instead of one .anyone please explain

  • @davidanatolie5407
    @davidanatolie54076 жыл бұрын

    What enables you to multiply probabilities like that in the baby example? Is it because the events J and N are independent? Is it a consequence of conditional probability?

  • @jbstatistics

    @jbstatistics

    6 жыл бұрын

    I state in the video "If we are sampling randomly and independently..." In other words, the events "the first baby has jaundice" and "the second baby has jaundice" are assumed to be independent. Whether that assumption is true would depend on the nature of the sampling.

  • @academichelp8738
    @academichelp87387 жыл бұрын

    can we convert set of data into uniform distribution

  • @hasannerneklitr
    @hasannerneklitr5 жыл бұрын

    It was very helpful. Thanks, man!!!! By HASAN

  • @jbstatistics

    @jbstatistics

    5 жыл бұрын

    You are very welcome!

  • @tamersahin5189
    @tamersahin51895 жыл бұрын

    Thanks!

  • @SeasideApothecary
    @SeasideApothecary2 жыл бұрын

    how did you get .6

  • @sauravsingh7271
    @sauravsingh72715 жыл бұрын

    YOU are too good....

  • @jbstatistics

    @jbstatistics

    5 жыл бұрын

    Thanks!

  • @tulasijamun3234
    @tulasijamun32346 жыл бұрын

    Isn't the plot at 10:55 a bar plot rather than a histogram?

  • @msfaqeelah7008
    @msfaqeelah70084 жыл бұрын

    Perfect 👌👌👌👌😍

  • @robynhall8805
    @robynhall88055 жыл бұрын

    Because the accuracy is governed by our measurement device, doesn't that make everything a discrete variable? e.g. if I'm measuring height, I may do so to the nearest cm or 0.5 cm, which then gives a countable finite number of possible values.

  • @aashishrana9356
    @aashishrana93562 жыл бұрын

    Super video

  • @fikrisaoudi7542
    @fikrisaoudi75428 жыл бұрын

    great work thnk you

  • @jbstatistics

    @jbstatistics

    8 жыл бұрын

    +Fikri Saoudi You are very welcome!

  • @bigboss.800
    @bigboss.8005 жыл бұрын

    Q on bivariate probability distribution And on distribution of sums and quotient

  • @user-yd5wv1st6u
    @user-yd5wv1st6u9 ай бұрын

    How did you get .4 when calculating the probability ?

  • @jbstatistics

    @jbstatistics

    9 ай бұрын

    The probability a randomly selected baby develops jaundice is 0.6 (as given in the problem statement). The probability a randomly selected baby does not develop jaundice is 1-0.6=0.4.

  • @muntadheralnoor8365
    @muntadheralnoor83655 жыл бұрын

    could you please explain how we got 0.6 for the probability of their occurring​??

  • @jbstatistics

    @jbstatistics

    5 жыл бұрын

    It was given in the problem. "Approximately 60% of full-term newborn babies develop jaundice" at 6:24.

  • @Tee2202
    @Tee22029 жыл бұрын

    how was 0.6 obtained for the example of babies with jaundice?

  • @TheTomboy345

    @TheTomboy345

    8 жыл бұрын

    Because 60% of newborn babies developed jaundice, 0.6 was given.

  • @gauravarya8952

    @gauravarya8952

    5 жыл бұрын

    Martian: you are right. During the course of the explanation, the 60% was somehow forgotten - which shouldn't have happened. Thank you for the answer.

  • @senpai1928

    @senpai1928

    5 жыл бұрын

    @@TheTomboy345 thank you, i know it was 3 years ago but i was just wondering this and paused to go in the comments section.

  • @TheTomboy345

    @TheTomboy345

    5 жыл бұрын

    @@senpai1928 You're welcome. :)

  • @usamanavid2044
    @usamanavid20444 жыл бұрын

    Thanks

  • @Cody-hz6jg
    @Cody-hz6jg2 жыл бұрын

    thanks bro

  • @briannahamilton1429
    @briannahamilton14295 жыл бұрын

    how did he get 0.6 for the probability of JJ?

  • @FB-tr2kf
    @FB-tr2kf6 жыл бұрын

    Can we say that each formula (such as the binomial, poisson etc...) is a Probability Mass Function?

  • @jbstatistics

    @jbstatistics

    6 жыл бұрын

    Yes, the formula that yields the probabilities for a discrete probability distribution is called the probability mass function.

  • @nm800
    @nm8005 жыл бұрын

    at. 13.37, is that a binomial distribution? If it is where does the 2 come from? Thanks!

  • @jbstatistics

    @jbstatistics

    5 жыл бұрын

    Yes, that's a binomial distribution with n = 2 and p = 0.6. (I don't discuss that in this video, as this video comes before a discussion of the binomial.) I'm not sure what you mean by "where does the 2 come from?", as it's just a simple example I picked with n = 2 and p = 0.6.

  • @nm800

    @nm800

    5 жыл бұрын

    @@jbstatistics Ok ok, I just thought that 0.6 comes from the fact that 60% of newborn babies developed jaundice whereas the number n should be the total number of the cases, right?

  • @jbstatistics

    @jbstatistics

    5 жыл бұрын

    @@nm800 Whoops! Yes, that's definitely the case. I just took a quick look last time, and didn't notice that I had a motivating example. I should have known better, as I almost always use a motivating example :)

  • @nm800

    @nm800

    5 жыл бұрын

    @@jbstatistics thank you very much. You're very kind. I like a lot your videos and I'm going to ask you a lot of things... sorry 😅

  • @jbstatistics

    @jbstatistics

    5 жыл бұрын

    @@nm800 You're welcome to ask, but I won't always answer :) If people ask for a clarification about a video concept, then I usually try.

  • @hajerjm
    @hajerjm5 жыл бұрын

    THANK YOUUUUUUUUUUU

  • @jbstatistics

    @jbstatistics

    5 жыл бұрын

    You are very welcome!

  • @AjayPatel-te4kb
    @AjayPatel-te4kb5 жыл бұрын

    Tq so much sir😊

  • @jbstatistics

    @jbstatistics

    5 жыл бұрын

    You are very welcome!

  • @preetiprasad3933
    @preetiprasad39335 жыл бұрын

    Thank you sir

  • @jbstatistics

    @jbstatistics

    5 жыл бұрын

    You are very welcome!

  • @NullPxl
    @NullPxl7 ай бұрын

    Even though height in the real world is continuous, whenever we actually model it wouldn't it be discrete since we can't measure height to infinite decimal places? Is what you're saying that there's a point at which if you have enough discrete datapoints, you can treat it as continuous?

  • @jbstatistics

    @jbstatistics

    7 ай бұрын

    I'm saying height, in its nature, is continuous. Absolutely anything that is truly continuous is subject to some sort of discretization based on the practical realities of the measuring device or method. Time, height, weight, etc. But yes, if we're not limiting ourself to a smallish number of possible values, it's usually reasonable to treat them as continuous. Sometimes how to treat a variable can be debatable, e.g. if we're taking medical measurements roughly each week, should we think of the # of weeks until occurrence of XXXX as discrete or continuous? Sometimes it's not obvious.

  • @NullPxl

    @NullPxl

    7 ай бұрын

    @@jbstatistics Thanks, that makes a lot of sense. Your videos have been very helpful during my stats course at waterloo :)

  • @nopecharon
    @nopecharon Жыл бұрын

    3:40 since this is infinite, this should be continuous right?

  • @jbstatistics

    @jbstatistics

    Жыл бұрын

    No, that's not the distinction between discrete and continuous. I included that intentionally, as an example of a discrete random variable that can take on an infinite number of possible values.

  • @pinkperiodic
    @pinkperiodic9 жыл бұрын

    THANK YOU! Many hours I spend wanting to biotch slap my teacher and yell "Get to the point! Keep it simple!" I've learned more here in 15 minutes than in hours of class. The only improvement I would suggests is some personality in your voice... kinda drone-ish.

  • @utkarsharane5146
    @utkarsharane5146 Жыл бұрын

    How do we get a probability of 0.6 for the kid getting jaundice?

  • @eduancloete5068
    @eduancloete50682 ай бұрын

    great intro, lets move on!

  • @vikramadi592
    @vikramadi5927 жыл бұрын

    next time while writing the description plz mention the duration of the playlist of each...

  • @TreBlass
    @TreBlass8 жыл бұрын

    What programming language do you use?

  • @jbstatistics

    @jbstatistics

    8 жыл бұрын

    The background is a Latex/Beamer presentation. I annotate using Skim and a Wacom Bamboo tablet. Screen capture and editing is done in Screenflow. Any statistical analysis or plots are done in R.

  • @TreBlass

    @TreBlass

    8 жыл бұрын

    Can you suggest me some sources where I can learn these languages? I have enrolled to a course for R on Edx, where can I learn more?

  • @maithlinair7161
    @maithlinair7161 Жыл бұрын

    Hi, how did you deduce probability of 0.6 and 0.6 for both babies having jaundice? A little unclear there

  • @jbstatistics

    @jbstatistics

    Жыл бұрын

    "Approximately 60% of full-term newborn babies develop jaundice."

  • @aalokkafle3989
    @aalokkafle39898 жыл бұрын

    I don't understand where the probability of 0.6 came from?

  • @sweetgal67

    @sweetgal67

    8 жыл бұрын

    +Aalok Kafle on the previous slide it gives a stat of 60% of newborns developing jaundice. so that is used to calculate the probability but none of the probabilities actually equal 0.6

  • @itzz_.alina_.shamgheta
    @itzz_.alina_.shamgheta2 ай бұрын

    I don't get how you got the probabilities e.g. the 0.6 and 0.4

  • @jbstatistics

    @jbstatistics

    2 ай бұрын

    It's given in the example. Approximately 60% of full-term newborns develop jaundice.

  • @El94Rey
    @El94Rey9 жыл бұрын

    please i want a lesson about expectation of a random variable

  • @jbstatistics

    @jbstatistics

    9 жыл бұрын

    It's next up in the playlist: kzread.info/dash/bejne/iK2fmqqKf8bReag.html

  • @Marius-vw9hp
    @Marius-vw9hp4 жыл бұрын

    9:45 "Dont worry, in MOST cases its not a MAJOR cause of confusion". Which means, usually, its at least a MINOR cause of confusion :p I definitely know it confuses me.

  • @aditishikha8149
    @aditishikha81493 жыл бұрын

    Might sound silly to a wizard like you but wanted to know why you list JN and NJ both as outcomes. Shouldn't they be the same thing. PLEASE HELP OUT SIR

  • @jbstatistics

    @jbstatistics

    3 жыл бұрын

    That's a reasonable question, and we all sometimes get trapped or confused on whether we need to pay attention to order or not. First note that I do eventually pool those together, as they are both the event that X = 1. But in the *calculation of probabilities* it's important to note that they are not the same occurrence. X=0 (JJ) can happen in only one way: The first baby selected must have jaundice, and the second must have jaundice. X=2 (NN) can happen in only one way: The first baby selected must not have jaundice, and the second must not have jaundice. But X = 1 can happen in two ways: The fist has jaundice and the second doesn't, or the first doesn't and the second does. Each of these has the same probability of occurring, and when we group them together into the event that X = 1, we need to account for that. If we look at the slightly simpler analog of flipping a balanced coin twice, if we ignored the ordering of the two possibilities that get us heads a single time (HT and TH), then we'd think we had 3 equally likely outcomes: Heads no times, 1 time, and 2 times. If these 3 were equally likely, then they'd all have a probability of 1/3. We know that can't possibly be the case, since the probability of getting heads both times must be 1/2*1/2 = 1/4. Our mistake would have been assuming that getting heads 0, 1, and 2 times were equally likely, when in reality getting HH, HT, TH, TT are the 4 equally likely outcomes.

  • @ahmedhamed2631
    @ahmedhamed26312 жыл бұрын

    Please can you translate to arabic Because I have problem with English

  • @dragonore2009
    @dragonore20096 жыл бұрын

    Who were the down votes from? Flat earthers that can't math?