Probability Exponential Distribution Problems

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  • Опубліковано 22 гру 2024
  • This statistics video tutorial explains how to solve continuous probability exponential distribution problems. It explains how to do so by calculating the rate parameter from the mean. It also tells you how to graph the probability density function.
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КОМЕНТАРІ • 189

  • @TheOrganicChemistryTutor
    @TheOrganicChemistryTutor  Рік тому +2

    Probability - Free Formula Sheet: bit.ly/3zb22rW
    Final Exams and Video Playlists: www.video-tutor.net/
    Next Video: ua-cam.com/video/CjF_yQ2N638/v-deo.html

  • @abdullahbabor4876
    @abdullahbabor4876 4 роки тому +51

    "Thanks again for watching" I mean why??
    Thank you, Professor!!!!!!!
    We all truly appreciate you and your time!

  • @harshparekh16
    @harshparekh16 2 роки тому +40

    Thank you so much man !! You have no idea how much you've helped me in learning statistics. The fact that you are providing all of this to us for free is just incomprehensible. Cheers man

    • @ktiwari31
      @ktiwari31 2 роки тому

      I think you intended to say ‘incredible’ and not ‘incomprehensible’.

    • @rosegold7283
      @rosegold7283 Рік тому

      @@ktiwari31 no they meant what they meant as in its so shocking its hard to understand how he does it

    • @rohithlohith9495
      @rohithlohith9495 Рік тому

      NO THEY MEANT IT AS ITS SO HARD TO UNDERSTAND WHY THEY WOULD GIVE THIS INFO FOR FREE@@ktiwari31

  • @mohammednayel8405
    @mohammednayel8405 5 років тому +43

    You are the best tutor i have ever witnessed... My doctor cannot explain with this brief way. your explanation even your voice really makes me yearn to watch more from your videos.... Thank God for your existence and may god rewards you
    ❤️❤️❤️🙏

  • @aravindssingapore4327
    @aravindssingapore4327 4 роки тому +47

    This video on exponential distributions has caused my knowledge on exponential distributions grow exponentially. Thank you 🙏🙏🙏🧬🍻

  • @Tnz_ira200
    @Tnz_ira200 2 роки тому +5

    I am so glad I came across this channel. Math generally isn't my best suit, but I am so happy youre helping me get there!

    • @DCSF15EPILOT
      @DCSF15EPILOT 8 місяців тому

      pretty sure this is statistics man

  • @travelingbutterfly4981
    @travelingbutterfly4981 3 роки тому +1

    U r the best UA-cam channel for learning. Ican find any videos I search for in your channel.u r Really great

  • @rajmrinal961
    @rajmrinal961 3 роки тому +14

    The last question where 4 < x < 7. I guess there is a small mistake in the equation. It should be e^(-0.8) instead of 1 - e^(-0.8). Since x is supposed to be greater than 4 and less than 7.
    Correct me if I am wrong please.
    Thank you!

    • @benjaminchirwa5445
      @benjaminchirwa5445 3 роки тому

      i think you are right

    • @nj-j7034
      @nj-j7034 3 роки тому +7

      Since the question asked BETWEEN 4 and 7 years. We can only use the differences between the area less than 7 and the area less than 4 to calculate the answer. (7:00) I believe e^-0.8 is the amount greater than 4. It makes no sense of differences between (the area less that 7) and (the area greater than4).
      If I have any errors, please correct me. Thanks

    • @diegoamores9295
      @diegoamores9295 3 роки тому

      Was thinking the exact same thing...

    • @naturindasheilla5246
      @naturindasheilla5246 2 роки тому +1

      I also realised that mistake

    • @elvocool
      @elvocool Рік тому +1

      I get what you're saying but in his case what he did is correct.

  • @xruan6582
    @xruan6582 4 роки тому +6

    Clear and concise, despite of tiny mistake at the beginning

  • @Tangawizii
    @Tangawizii 5 років тому +335

    I believe you made a mistake towards the beginning when calculating the value for lambda. You wrote "lambda = 1/lambda" instead of "lambda = 1/mu"

    • @chinchang5117
      @chinchang5117 4 роки тому +15

      Of course, the teacher has made a mistake. But it is up to the student to correct the mistake himself.

    • @Nova-Rift
      @Nova-Rift 4 роки тому +84

      @@chinchang5117 wrong

    • @leothompson6397
      @leothompson6397 4 роки тому +31

      ​@@chinchang5117 Ironically, you are the person who is wrong here. What you said applies to entire subjects, as in, the student needs to discover the things that the teacher could not. It does not mean that during teaching, the teacher can stack up minor mistakes without care.. Know when to apply your knowledge.

    • @afonsoeira5
      @afonsoeira5 3 роки тому +6

      @@chinchang5117 u got finessed

    • @melonmelonmelon8422
      @melonmelonmelon8422 3 роки тому +3

      @@chinchang5117 I am surprised that no one said anything about his username? so Disrespectful

  • @morganolivianewton8061
    @morganolivianewton8061 Рік тому +2

    Thanks!

  • @dorcaskaunda9016
    @dorcaskaunda9016 3 роки тому +3

    Simple and straight forward,u have made my life so simple in med school 🙏thank you

  • @imaneboualam6000
    @imaneboualam6000 5 років тому +1

    You have been so helpful every time I feel a struggle. But today I am here just to hear your voice.

  • @reena3571
    @reena3571 Рік тому +1

    I recently discovered your channel and I must confess that it has been super resourceful. I have had trouble understanding some theories and concepts in statistics. Mind you, I have been done with Uni for years. However, because I want to purse a career in Data science which requires having fundamental knowledge of some area of statistics makes it an evitable challenge that I must overcome in order to excel in this desired field. Great Job!

  • @NK-iy6if
    @NK-iy6if 2 роки тому +1

    God bless you, Thank God for leading me to your channel. Thank you for the videos

  • @fatimaalromaithi3147
    @fatimaalromaithi3147 4 роки тому +6

    Amazing lesson! thank you! I found a difficulty in the material but you made it really easy!

  • @ktiwari31
    @ktiwari31 2 роки тому +27

    In first minute lambda = 1/mu you have made a typo there.

  • @rainberry_x
    @rainberry_x 4 роки тому +1

    What would I do without this man🥺🥺🥺

  • @pedrogaleano6722
    @pedrogaleano6722 4 роки тому +1

    Very useful! Thank you very much! You saved me hours of trial and error trying to figure out what this kind of problems were about!

  • @vford1000
    @vford1000 5 років тому +3

    Another Great Video, you explain things so well that's easy to understand!

  • @HuriaSaboori
    @HuriaSaboori Рік тому

    Another helpful video, very excited for my Statistics test.

  • @halasentissi
    @halasentissi 6 місяців тому +1

    YOU ARE A LIFE SAVEEEEEEER !!!!!!!!!!!

  • @easonsun4030
    @easonsun4030 3 роки тому +1

    i am from a top 30 university and I still think you are way better than my professor

  • @RafiqulIslam-un9zp
    @RafiqulIslam-un9zp Рік тому

    You're really good at explaining things easily. Keep up the good word.

  • @hcapppp
    @hcapppp 3 роки тому

    Great video, helped a lot, greetings from Sweden!

  • @lamecksigauke4595
    @lamecksigauke4595 2 роки тому

    You have been a life saver dude

  • @ephraimacksonmumba14
    @ephraimacksonmumba14 2 роки тому

    thank you so much and i rate you all the stars in the galaxy and universe at large you are the best.

  • @morganolivianewton8061
    @morganolivianewton8061 Рік тому

    As always, you're the best. TY.

  • @aravindssingapore4327
    @aravindssingapore4327 4 роки тому +11

    Hi, brother.
    I think you meant:
    Now, the rate parameter is going to be 1 over miu, not one over lambda

  • @A_k_h_i_l_007
    @A_k_h_i_l_007 Рік тому +2

    1:00 its 1/MYU RIGHT

  • @husseinalhadi5471
    @husseinalhadi5471 Рік тому +2

    Hi for part (e) shouldn't x be Greater than 4 and less than 7, was that a mistake?

    • @jonassherman9251
      @jonassherman9251 9 днів тому

      No, because when you solve for the area of the graph for x (less than) 7, you are finding the area of the graph from x=0 to x=7, meaning that the area between 4 and 7 is already accounted for, but the area between 0 and 4 is also counted in that. So you have to subtract the area from 0 to 4 to get only what is between 4 and 7. hopefully that made sense.

    • @jonassherman9251
      @jonassherman9251 9 днів тому

      I just realized that this comment was from a year ago and you probably either no longer care about the solution or you figured it out haha. anyway, in case you were still wondering... there it is🤣

  • @guymondgopolang8894
    @guymondgopolang8894 5 років тому +1

    You never disappoint. Thank you

  • @josephlumpa5015
    @josephlumpa5015 Рік тому

    Thank you so much Sir, you have really helped me in studies.

  • @uavidavida7633
    @uavidavida7633 2 роки тому

    Thank you for sharing this video. I was watching my class lecture and just did not get it. I also didn't realize I needed to use the "power of e" on the calculator to get the number.

  • @vaibhavgiria5997
    @vaibhavgiria5997 4 роки тому +3

    5:07 shouldn't the func be 0.20e^-(0.20X) missing 0.20 only e^-(0.20X)

    • @PJURALszymon
      @PJURALszymon 4 роки тому

      true!

    • @frankbarboza
      @frankbarboza 4 роки тому

      No, because at around 5:07 he is calculating the area to the right of 10. This is different from F(x) which gives us only the height above the curve but not the area; two different calculations.

    • @teja1853
      @teja1853 4 роки тому

      @@frankbarboza I am still confused. The PDF calculated here is: 0.20e^-(0.20X). But to calculate the probabilities, the equation used is: e^-(0.20X). Can someone explain me this?

    • @frankbarboza
      @frankbarboza 4 роки тому +2

      @@teja1853 The PDF is used to calculate a single point (height) above the curve. When X is 0, the height above the curve is 0.20; when X is 10, the height above the curve is 0.02706 (I just substituted 10 for X in the equation you typed in your reply). The CDF is used to calculate the probability (the area). When calculating the area to the right of a critical point, use e^(-lambda multiplied by X); when calculating the area to the left of a critical point, use 1 minus e^(-lambda multiplied by X).

    • @teja1853
      @teja1853 4 роки тому +1

      @@frankbarboza Thanks for explaining! I understand it now

  • @duongminh1972able
    @duongminh1972able 2 роки тому

    Thank you for your explanation, I understand it better through your example. Previously I read the formulas but did not feel how this distribution get the specific value corresponding to X= time.

  • @reamabdulsalam524
    @reamabdulsalam524 Рік тому +3

    Statistics is very difficult and really confusing and too much information are given so please do explain the formula of getting lamda from the mean and also in one of your videos you calculate lamda=1/lamda ?? Is it 2/lamda or 1/mue ? Or mue=lamda time t ???

  • @reamabdulsalam524
    @reamabdulsalam524 Рік тому

    Hello your channel is amazing and I never go to any other tutors to understand my problem but please do explain when we use each distribution as there are many of questions they don’t tell you the distribution type so you have to guess and stay in doubt and also when you are calculating lamda or mue too many books has introduce it in different ways and it is so confusing so when we have the mean please clearly explain how we can calculate lamda thanks

  • @tinakwok7600
    @tinakwok7600 2 роки тому

    you save my life.

  • @aishaabdi891
    @aishaabdi891 3 роки тому +1

    its has been an amazing lesson thank you

  • @MindMathMoney
    @MindMathMoney 5 років тому +1

    Love you! ❤️❤️

  • @wispeidolon3422
    @wispeidolon3422 4 роки тому +1

    btw you can also calculate the area under the curve with integrals since we know the formula

  • @sayemshah7520
    @sayemshah7520 2 роки тому +5

    Why is there 1- in (1-e)

  • @sandramanyarkiy751
    @sandramanyarkiy751 5 років тому +2

    Hello, is it always stated that the problem will be of exponential distribution, and if not could you give an example of a problem? Thanks.

    • @henrykashyap8913
      @henrykashyap8913 Рік тому

      Always coz there are many ways of distribution....

  • @Tomatocheesepizza
    @Tomatocheesepizza Місяць тому

    6:21 shouldnt that be P(x>4) ?

  • @aadibmafaz8702
    @aadibmafaz8702 2 місяці тому

    i don't get the first question option c, why do we need to subtract with 1, isn't the probability of adding f(0) , f(1), f(2) right would be the answer?

  • @virajkapur8366
    @virajkapur8366 Місяць тому +1

    hows this guy carrying my statistics as well

  • @freeandeasy9795
    @freeandeasy9795 3 роки тому

    Clearly explained. Well done, and thank you!

  • @franciscaaidoo5095
    @franciscaaidoo5095 9 місяців тому

    please what is the mean for the exponential distribution when theta is given instead of lambda?

  • @emadharazi5044
    @emadharazi5044 4 роки тому +2

    Another great video. Thank you.
    I was, however, hoping you would include an example question that involves the less than and equals sign or more than and equals sign. I thought that if we wanted to know the probability of a laptop lasting a week or more (which each event being a day), we could simply make x=8 and use the greater than sign but it doesn't seem to be right.

    • @TheCoKeys
      @TheCoKeys 4 роки тому +2

      Kinda late but just in case when the less than and equal or more than and equal signs are used in distributions that are continuous(i.e. not discrete) it is essentially irrelevant and it is calculated the same way as if it was just a regular bigger than or smaller than 'x'.

  • @li_themizfit_il
    @li_themizfit_il Рік тому +6

    btw its x is greater than 4, not x is less than 4

  • @joachimnyirongo1627
    @joachimnyirongo1627 2 роки тому

    How can one proof that exponential distribution of independent variables can lead to poisson distribution?

  • @lambertothieno3386
    @lambertothieno3386 2 роки тому

    How are these videos so helpful!!!!

  • @amyeskelsen8237
    @amyeskelsen8237 3 роки тому

    Thank you so much! This was really helpful.

  • @umairfarooq7557
    @umairfarooq7557 3 роки тому +4

    I believe you made a mistake towards the end because
    P (4

    • @mouinemhb4960
      @mouinemhb4960 2 роки тому

      i know this is way too late but you forgot to put the 1- in the second part
      so shouldve been 1- e...

    • @rodyabd5355
      @rodyabd5355 2 роки тому

      @@mouinemhb4960 Late response. You don't need to put 1 in the second part, because, you are calculating (0-4) whereas in the first part you are calculating (7-inf). So, the (1 - ) is just to calcuate the compliance

    • @L.O.L.Adventures
      @L.O.L.Adventures 4 місяці тому

      yep your answer is correct.i also got 0.30407

    • @krishnendubanik3026
      @krishnendubanik3026 Місяць тому +1

      @@L.O.L.Adventures but i think that the video is correct and this comment section is wrong. Since we need to find X b/w 4and 7 we need to find the left side are of 7 and substract it with the left side area of 4 to get the answer. So, P(X

  • @shruthilayak4988
    @shruthilayak4988 7 місяців тому

    I have a doubt is that shoukdn't we be doing integration using the given years/time as limits?

  • @franciscaaidoo5095
    @franciscaaidoo5095 9 місяців тому

    Please is theta the same as lambda when given a question?

  • @yuratea1700
    @yuratea1700 4 роки тому +6

    But doesn't the problem say BETWEEN 4 and 7 years, meaning MORE than 4 and less than 7, not LESS then 4 and less than 7?

    • @stevencarrell83
      @stevencarrell83 4 роки тому +1

      That's what I worked out. So i'm hoping he made a small error on this and we are correct

    • @aavishkarsingh6719
      @aavishkarsingh6719 4 роки тому

      Yeah, what's up with that ?

    • @khangelanimgqibelo3000
      @khangelanimgqibelo3000 4 роки тому

      I thought it that way too, but if i am correct then that would mean the answer is 0,3041.

    • @reecej3228
      @reecej3228 4 роки тому +3

      7:00 he explains it here

  • @dmitrikorin3033
    @dmitrikorin3033 5 років тому +2

    Amazing tutor video, only thing I feel like you should be following more "standard practice" that mathematicians use, like when you show us P(x

  • @msdmsd2502
    @msdmsd2502 9 місяців тому +2

    bro there's a mistake in 1:04....lambda=1/mean....you wrote it as lambda=1/lambda....please see to it

  • @larryschwartz478
    @larryschwartz478 3 роки тому

    I'm having trouble understanding the probability density function for the exponential distribution. What does it mean to say that the event at time=0 has a positive probabilty? I had thought that no event occurred at that time, so its probability should be zero. Why not?

    • @ryanjackson0x
      @ryanjackson0x 2 роки тому

      Time=0 is when we started measuring. In this example I believe it is when all of the laptops are functioning properly, and as time progresses, they start failing with a rate given by the distribution function.

    • @larryschwartz478
      @larryschwartz478 2 роки тому

      Thanks very much for your reply. I had already looked into this further. My question to you was about the continuous exponential density function, although I had not mentioned it because I usually think in terms of continuous densities. I have discovered that for any continuous density P, P(X) = 0 for all X. I had never thought about this before. It reflects the fact that in a continuous density, X must be defined exactly. If X is, say, weight, and we ask what is the probability that someone's weight is 150 lbs., the continuous density will give that probability for exactly 150 lbs. However, no one weighs exactly 150 lbs. so P(150) = 0. But the probability of someone weighing between 150 lbs and 150.1 lbs can be obtained from the cumulative probability density of P. So, for a continuous exponential distribution, the probability of an event occurring at time=0 is really 0 because, literally, no event can really take place at time=0. But if we really mean the short interval between time=0 and time=30 seconds, then we can get the correct probability from the CDF. I learned a great deal from your video and the extended search it led me to. Thanks again, Larry Schwartz

  • @keldonchase4492
    @keldonchase4492 5 років тому +1

    Did he mean to say that lamba is defined as one over mu? Can somebody clarify? Thank you

  • @nmesomiladyobi5825
    @nmesomiladyobi5825 10 місяців тому

    I have a question concerning (E)
    You wrote that X is less than 4
    I thought X should be greater than 4

  • @dimitriysevryukov1629
    @dimitriysevryukov1629 Рік тому

    Thank you very much !

  • @pedrofernandes4050
    @pedrofernandes4050 4 роки тому +2

    Is it right to do P(47)?

  • @austinbaum1753
    @austinbaum1753 3 роки тому

    THANK YOU SO MUCH! litterally about break sth over this stupid math problem

  • @zhou6075
    @zhou6075 2 роки тому

    clear and helpful

  • @Ppooh002
    @Ppooh002 2 роки тому

    are the formulas applicable whether the interval is inclusive or not?

    • @Peter_1986
      @Peter_1986 2 роки тому +1

      Yes, they should be applicable, because in this situation you are calculating continuous values, and one single specific value has a 0 chance of occurring, since it is one out of an infinite number of values.
      So "x ≤ a" and "x < a" would actually mean the same thing, since P(x = a) = 0.

  • @masterara9361
    @masterara9361 5 років тому +1

    solid follower here

  • @khemramneega5901
    @khemramneega5901 2 роки тому

    wow that easy, thanks dude

  • @noworries838
    @noworries838 3 роки тому +1

    life saver

  • @Lolsade6
    @Lolsade6 5 років тому +1

    Can u make a video about integral problems in physics because that’s my first test in ap physics and I haven’t taken calc yet. Keep up the great work 👍

    • @saki7952
      @saki7952 5 років тому

      He already uploaded.

  • @haleisreading123
    @haleisreading123 2 місяці тому

    this could be an obvious answer but why aren't we using integrals in these cases?
    Like with the one less than 3, can't we just do integral [3, 0] f(x)?

  • @astropeanutcat1953
    @astropeanutcat1953 3 роки тому

    Thank you for thi one!!!!

  • @pandurangnaik9291
    @pandurangnaik9291 3 місяці тому

    Thanks 👍

  • @dr.pravinvadhel4183
    @dr.pravinvadhel4183 3 роки тому

    The income tax of man is exponentially distributed with f(x) = 1/3*e^(-x/3) ;x>0. what is the probability that his income will exceed rs. 17000? assume that the tax is levied at the rate of 15% on the income above rs. 15000.

  • @maryamaishanyc7449
    @maryamaishanyc7449 4 роки тому

    Why are you saying y/lamda but where did you get what lambda = to?

  • @BH-he3wg
    @BH-he3wg 2 роки тому +4

    i dont understand why it was .20yrs ^-1 in the first problem

  • @Abdelrahman_Hosny
    @Abdelrahman_Hosny 2 роки тому

    Thanks a lot

  • @Shaan11s
    @Shaan11s 3 місяці тому

    When I see an Orgo video, I know everythings gonna be alright

  • @maliamungubenard1896
    @maliamungubenard1896 2 роки тому

    i have understood exponentially

  • @milareal2035
    @milareal2035 8 місяців тому

    THANK YOU

  • @bikitachapters.kudzaichika4863
    @bikitachapters.kudzaichika4863 8 місяців тому

    You are great

  • @tau1650
    @tau1650 5 років тому

    you are the best I the world j g

  • @Maharrami
    @Maharrami 2 роки тому

    Amazing!

  • @kayodeashaolu7036
    @kayodeashaolu7036 3 роки тому

    Thanks

  • @kiz6071
    @kiz6071 4 роки тому

    thanks a lot!

  • @mystique973
    @mystique973 Рік тому

    gud explanation

  • @harukiii2005
    @harukiii2005 6 місяців тому

    I think there is no correction for the question between 4 and 7 years. Knowing that the area of P(4

    • @harukiii2005
      @harukiii2005 6 місяців тому

      This is just something I've noticed from the comment section (I know it's very late to point this out)

  • @yakubumawrud1470
    @yakubumawrud1470 9 місяців тому

    The last part is it not supposed to be x>4 instead x being less

  • @dr.downvote
    @dr.downvote 3 роки тому

    What is P(X=x)?

    • @ryanjackson0x
      @ryanjackson0x 2 роки тому

      For any continuous random variable, 0.

    • @davidsling
      @davidsling Рік тому

      u cant get exactly one point cuz it use continuouse varibale that same for any continuouse nummer like P{X=3.32542623}=0

  • @tatianaletourneau602
    @tatianaletourneau602 4 роки тому

    againnn u da bestttt

  • @treysean4778
    @treysean4778 2 роки тому +1

    if no one got me, i know the OCT got me

  • @coulie27
    @coulie27 4 роки тому

    Fantastic

  • @khushbukotwal3481
    @khushbukotwal3481 2 роки тому +1

    in last answer you have written x

  • @powenworth1041
    @powenworth1041 2 роки тому

    Part c where x

  • @claudiamesaaparicio8517
    @claudiamesaaparicio8517 4 роки тому

    bravo!

  • @kamanzifelixssuna5914
    @kamanzifelixssuna5914 3 роки тому

    I think P(4

  • @calebkelly7225
    @calebkelly7225 2 роки тому +2

    There is a mistake at the end of the Video it should be x>4 and x

  • @santiagotrujillo6253
    @santiagotrujillo6253 3 роки тому

    thanks :)