Excellent explanation. Your explanation for function of a random variable is the best one I have seen so far. Your students are blessed to have. Please post more probability Videos because probability is not very well explained by a lot of professors making concepts in probability theory even more confusing. Thanks once again. God bless. you.
Thank God for this video. My professor is beyond incompetent at explaining this topic and my textbook glosses over it without showing the underlying principle. I should have went to MIT for my EE degree.
Thanks! Gosh - I wish my professor liked to use small, straightforward examples instead of using the most abstract and general form possible. It's strange that application can teach theory, but not always the same way around.
+WateryIce54321 theories are the result of extensive expirements witnessed first hand and their 'general' behaviour noted. if you teach a student theory first, you are letting go of the process that actually led to the theories being understood. for a new-comer, teaching theory first is IMO the worst way to make someone understand. the general and abstract form is only good for someone who already knows the process. something very few instructors/books realize
@Ahmed! excellent!!! thank you so much 4 pointing that out. Intuition is what is most missed! :-) Basically what you are saying is: One cannot think abstractly without having (concrete) examples from which one can filter the most important Connections.
@@andrewagita901 correct.. Its kinda hard to learn when my professors mic kept cutting out to the point I couldn't understand but 2-3 words a sentence and he refused to articulate.
So what is the mapping from the sample space? I thought the professor said the random variable, for example in this case X, maps "stuff" from the sample space to the real number line of x.
Presumably, the outcomes in the sample space were used to generate the PMF we see here. So instead of starting with the sample space and then calculating the PMF for X from it, we are just given the PMF. In some sense, though, we can view the values of X as our new sample space.
Nice explanation. However, while calculating PMF of Z for all k values, why k=0 is taken? Z can never take 0. 0 belongs to the set of values X can take. If we look at the set of values Z can take, it is {9, 4, 1}.
The link to the complete course does not work anymore. This is the complete playlist on TH-cam: th-cam.com/play/PLUl4u3cNGP60A3XMwZ5sep719_nh95qOe.html .
Thanks for the note, we will fix the redirect. The redirect is supposed to go to: ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-041sc-probabilistic-systems-analysis-and-applied-probability-fall-2013/. Best wishes on your studies!
A probability mass function differs from a probability density function (pdf) in that the latter is associated with continuous rather than discrete random variables; the values of the latter are not probabilities as such: a pdf must be integrated over an interval to yield a probability.
I don't understand why Z isn't squared again. Z = X^2, so you square all of X's possible values. (Makes sense, okay.) Then, you put these possible values in the numerator above "a." (That makes sense, because X/a was what we did to make the original PMF.) Yet, then you just union them? Like, I don't understand the logic behind that? What happened to x^2 in the numerator of the original PMF? Where is the indication that (9/a ,9/a) should be summed now?
Dustin Black it’s not just this case that doesn’t make sense in probability, there are a bunch of other cases where i’m trying to make logic of what i’m seeing but nature is more complex than we think 🤔
You're very good at explaining things. Thank you very much.
My professor should be paying you for these videos.
Excellent explanation. Your explanation for function of a random variable is the best one I have seen so far. Your students are blessed to have. Please post more probability Videos because probability is not very well explained by a lot of professors making concepts in probability theory even more confusing. Thanks once again. God bless. you.
Thank God for this video. My professor is beyond incompetent at explaining this topic and my textbook glosses over it without showing the underlying principle. I should have went to MIT for my EE degree.
Thanks! Gosh - I wish my professor liked to use small, straightforward examples instead of using the most abstract and general form possible. It's strange that application can teach theory, but not always the same way around.
+WateryIce54321
theories are the result of extensive expirements witnessed first hand and their 'general' behaviour noted.
if you teach a student theory first, you are letting go of the process that actually led to the theories being understood.
for a new-comer, teaching theory first is IMO the worst way to make someone understand.
the general and abstract form is only good for someone who already knows the process. something very few instructors/books realize
cant agree more
@Ahmed! excellent!!! thank you so much 4 pointing that out. Intuition is what is most missed! :-)
Basically what you are saying is: One cannot think abstractly without having (concrete) examples from which one can filter the most important Connections.
This!!!
@Asymptote: Bro what you mean by "This!!!" ?
This makes way more sense, i just learned more watching this video than i have the entire semester in my statistics class.... Thanks
so u learned nothing
@@andrewagita901 correct.. Its kinda hard to learn when my professors mic kept cutting out to the point I couldn't understand but 2-3 words a sentence and he refused to articulate.
Finally, I found the tutorial and teacher I was searching for! great explanation!!
Great video although I believed you lacked the final and most important thing, how is Pz(K) written? Pz(K) = 2k/28 for values 1, 4 and 9.
One of the best explanation!
Fantastic explanation. Thank you.
Crystal clear!
This was explained very clearly! Thank you ❤️
Very intuitive class! Congratulations and thank you very much!
Is there a better way to calculate this, such as plugging z into the pmf of x, or something similar?
how to find sum of two dependent random variable pmf
Perfect explanation.....
So what is the mapping from the sample space? I thought the professor said the random variable, for example in this case X, maps "stuff" from the sample space to the real number line of x.
Presumably, the outcomes in the sample space were used to generate the PMF we see here. So instead of starting with the sample space and then calculating the PMF for X from it, we are just given the PMF.
In some sense, though, we can view the values of X as our new sample space.
Nice one can you make a lecture of finding the value of constant k given the pmf please
Loved the easy explanation keep up the good work 😊
9:00 Hey shouldn't z take on values of { (-3/28)^2, (-2/28)^2... } ???
The sum wouldn't equal one.
02:51
you too ♥
10:03 also.
Can anybody explain why -1 wasn't in the sum notation then a should be 29
This was super helpful! Thank you so much!
Nice explanation.
However, while calculating PMF of Z for all k values, why k=0 is taken? Z can never take 0. 0 belongs to the set of values X can take. If we look at the set of values Z can take, it is {9, 4, 1}.
She explained why: 0 would be for the "otherwise" case.
So nice and simple to understand ..thanks
IF it was Z= X^2/2 instead of Z= X^2, then Z would have taken values like 1/2 and 9/2. Are these values a valid value?
Yeah, why not?
@@saeidakbari4788 maybe he got confused because these are called discrete random variables
The link to the complete course does not work anymore.
This is the complete playlist on TH-cam: th-cam.com/play/PLUl4u3cNGP60A3XMwZ5sep719_nh95qOe.html .
Thanks for the note, we will fix the redirect. The redirect is supposed to go to: ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-041sc-probabilistic-systems-analysis-and-applied-probability-fall-2013/. Best wishes on your studies!
perfect explanation. thank you
Okay but how do I get the PDF of that PMF? Why do my teachers always have me doing stuff that you can't find videos on???
A probability mass function differs from a probability density function (pdf) in that the latter is associated with continuous rather than discrete random variables; the values of the latter are not probabilities as such: a pdf must be integrated over an interval to yield a probability.
Wikipedia
simple and clear!! thank you!
Awesome explanation. Perfect. Thank you!!
Excellent video.
Thank you for the explanation
God Bless you! Thank you!
great explanation
nice explaining and very good example ..
excellent, Katie. very understandable.
Very helpful. Thanks !
why (28/a)=1?
I need a tutorial regarding EPA-PMF software. How its run and useful for groundwater source apportionment.
i need help.
thank you so much omg you snapped
VERY UNDERSTANDABLE
Well done!
today is my exam u just saved my day ....thanks :-)
Thank you so much!❤
Thank you very much :)
so helpful.tank you so much
Thank you, it helps me a lot.
God bless you 🙏🦃
nice explanation
miss your explanation is out class
O my GOD Where have u been since i am shitting my mind...........
Great Very Great .......
p(x)=1/8,-4
i learned, finally.
Splendid Splendid more than Splendid
I 've downloaded Course materials thank you M.I.T, I wish I could donate but is not pass
OMG ITS VELMA FROM SCOOBYDOO!
I don't understand why Z isn't squared again. Z = X^2, so you square all of X's possible values. (Makes sense, okay.) Then, you put these possible values in the numerator above "a." (That makes sense, because X/a was what we did to make the original PMF.) Yet, then you just union them? Like, I don't understand the logic behind that? What happened to x^2 in the numerator of the original PMF? Where is the indication that (9/a ,9/a) should be summed now?
Agreed. Shouldn't it remain x^2 / a? The answer should remain the same in this case, but the method wouldn't.
Dustin Black it’s not just this case that doesn’t make sense in probability, there are a bunch of other cases where i’m trying to make logic of what i’m seeing but nature is more complex than we think 🤔
thankyou very much
I think I'm on my PMF.
can you predict random matrics using this concept
thats amazing
your voice😍😍😍🥰🥰🥰
Very clear~!Thank you~!
Smart and wearing glasses: My favorite kind of woman.
OMG I LOVE YOU LADY
wow
💗
ablam ne anlatıyor sen allah için
u re magnificent
wt ha ha every time