What he is actually doing is showing that the area of the smaller and smaller rectangles converge to the probability P(X=3). And the sequence of numbers, 1/25, 1/250, 1/2500, ... (1/[25*10^n]) converges to zero. If you want to express 1/∞ as the result of that limit. 1/∞ = 0.
wow i watched your videos in 2019, and it really interesting when came to philosophical answer of question why the probability of exact value of X should be 0. you did great job sir.
Really struggling in an intro Statistics class for health care and these videos have helped a lot. Can you point me to any videos that would refresh me on how to manipulate inequalities like this? I'm so lost trying to determine something like finding the standard normal variable z for P(-z0 < z < z0) = 0.9442. We're just using a table for standard normal distribution (z) values in the textbook since calculus is out of the scope of the course. I took Math A30/B30/C30/Intro Calculus in high school but haven't touched any of that since 2004 or so. Can someone help me?
That's using the decimal system, decimal systems have the greatest rate (convergence?) to infinity. What if everything in the universe is countable? I think that chances are if it involves probability the area in that rectangle is all countable so it should be using fractions.
Thanks a lot for the great intro! I'm trying to get my head around the fact, how every single event can have a probability of 0 thus being an impossible event but still occur? Is it a definition or is it somehow grounded in reality? A continuous probability distribution can be interpreted as the prediction of rolling a fair dice with an infinite amount of sides, right? Then the probability of rolling each number would be zero, but still, every roll would show a number... an impossible event would have occurred, right? Thank you all in advance!
Rolling a die is NOT a continuous probability distribution (CPD) but rather a discrete problem. For a CPD, it is impossible to get exactly an event. Imagine, the probability of a person being exactly 180 centimeters. It is almost impossible to be sure of that down to the atomic level. They can be 180.000000000...1 cms. But, we can be sure that they are between a certain range for instance between 179.99 and 180.01. This is not the case with the dice as they can only be one of 6 different events (1, 2, 3, 4, 5, 6). To summarise, continuous variables can only occur in a certain range. On the other hand, discrete variables, for example, rolling a die can occur as an exact event. I hope I was clear!
something which doesn't make sense to me about the final point... if the probability of each single number occurring is 0, then how is the sum of all the numbers 1..
its very simple. Imagine that you are about to collect water from an ocean. The probability of getting a specific drop is close to almost zero(much similar to the limit theorem in calculus). But think about collecting say 10 litres, 100 litres or 1000 litres of water. You can see the probability increases. This is what I understood and it makes sense to me.
We're using the fact that the sum of the probability of all the events is 1. As we're dealing with a density function where the area under the curve is the probability of that function, we use the formula for the area of a rectangle and equate it to one. You're getting confused between a PDF and a CDF. In a PDF the range of the function isn't bounded, the only condition that it has to follow is that the total probability is 1. Whereas for a cdf of a continuous random variable (as is the case here) the individual probability is 1/infinity, that is zero. Hope that this clears your doubt, else I'd strongly advice you to rewatch the video on what exactly is a pdf and what exactly is a cdf. Sal does an amazing job at this.
This guy is brilliant ... I just can't stand the fact he repeats himself so much. "Under the curve" ... "Under ... The cuuurve , Under the curve", I am always giggling to myself when he does that and he does that often. :/
You can't do that. There are infinite numbers from 0 to 5, which is why the probability of an exact number is 0. However, since the function is defined from 0 to 5, the probability of some number in this range is 100%. Does that make sense?
@@GLu-tb1pbI'm not sure I understand. Lets say I randomly chose a number X between 1 and 5. Then I asked you what the probability of me randomly getting X. The probability of me getting exactly X is 0% yet somehow I still got X. The odds of getting X are 1/C as C approaches infinity. wouldn't the probability approach zero but never get there
As usual didnt explain the most importnat bit, why da hell probabulity of a exact value become zero, what is the explanation using probabilty, not using graphs?
+Amy Tan Imagine you are weighing a piece of meat with a tool and the weight is equal = 1 KG. If you want to treat this tool as the most perfect tool so the weighing process is no longer treated as a random event and you don't need the probability theory anymore. But some one may say that the tool is just a normal tool and it's of course inaccurate by a certain degree. Accordingly you'll assume that the real weight is = 1.X KG and since the tool is not too accurate it weighs only 1 KG. 1.X KG What are possible values of x ? the answer is from 0 to 9 What is the probability for x to be = 0 ? the answer is 1/10. What is the probability for that piece of meat to be equal 1.0 KG Exactly ? the answer is 1/(10^1) Now, some other smart guy should ask you why you assumed that the real weight of that piece of meat was 1.X ? it is actually 1.XXXXXXXXXX KG (10 decimals) but your tool just read it 1 KG and neglected the other decimals. 1.XXXXXXXXXX KG (10 decimals) What are possible values of x ? the answer is from 0 to 9 What is the probability for the 10'X'es to be = 0 at the same time ? the answer is 1/(10^10). What is the probability for that piece of meat to be equal 1.000000000 KG Exactly ? the answer is 1/100000000000 So we can put in general mathematical form P(Exact Number) = (1/10^a) , Where 'a' expresses to what extent you believe that there are more decimals existing than you can really measure. Hope it helps
+Amy Tan When you have 2 objects, the probability of getting one of them is 1/2. When you have 3 objects, the probability of getting one of them is 1/3. Now here you have an infinite amount of objects, so the probability of having an exact value will be (1/n) with n going to infinity, the reciprocal of a very big number is one that gets closer and closer to zero, so at the end the reciprocal of a number going to infinity, will be zero. I hope this answered your question if something wasn't clear feel free to let me know.
![SahBabii - Viking [Official Music Video]](http://i.ytimg.com/vi/D37cL92JX0I/mqdefault.jpg)
What he is actually doing is showing that the area of the smaller and smaller rectangles converge to the probability P(X=3). And the sequence of numbers, 1/25, 1/250, 1/2500, ... (1/[25*10^n]) converges to zero.
If you want to express 1/∞ as the result of that limit. 1/∞ = 0.
wow i watched your videos in 2019, and it really interesting when came to philosophical answer of question why the probability of exact value of X should be 0. you did great job sir.
Started my revision for Continuous R.Vs today. I was so chuffed when this popped up in my subscriptions!
Justin Kirk is a math expert? You learn something new every day ...
Yours are the best math videos on the web... thank you so much.
Give this guy a Arcom medal ! Salute.
Excellent.Leads naturally to the bell shaped curve.
awesome discription given.. best for core concept
... It got pretty interesting in the end hahahahaha
Awesomely interesting stuff! Thank you very much, sir.
I love the way you teach
43 and still learning, thanks Sal
Solid explanation ... making a pattern and lastly proving the pdf at an integer value is 0. Thumbs up
Very good explanation sir
You're the best so far .Thank you :)
Very good explanation... as always
Very helpful video with great visualization! Thank you!
very helpful .............goooood job
You never disappoint me dude, keep up the good work.
Very well explained.
just amazing, got all of that in one run...
Really struggling in an intro Statistics class for health care and these videos have helped a lot. Can you point me to any videos that would refresh me on how to manipulate inequalities like this? I'm so lost trying to determine something like finding the standard normal variable z for P(-z0 < z < z0) = 0.9442. We're just using a table for standard normal distribution (z) values in the textbook since calculus is out of the scope of the course.
I took Math A30/B30/C30/Intro Calculus in high school but haven't touched any of that since 2004 or so. Can someone help me?
It's time to bring back some long lost memories! 😄😆😂
continuous random probability is like area
Thank you for the detailed explanation!
beautifully explained
Great Job!
Thank you very much
You are awesome dude! Thanks!
great stuff
thank u sir good explanation
The last part just blew my mind lol
YES STATS! PERFECT TIMING!
That's using the decimal system, decimal systems have the greatest rate (convergence?) to infinity. What if everything in the universe is countable? I think that chances are if it involves probability the area in that rectangle is all countable so it should be using fractions.
thanks for explaining this! That was very well done!
Fantastic..
Thank you!
Thanks a lot for the great intro!
I'm trying to get my head around the fact, how every single event can have a probability of 0 thus being an impossible event but still occur? Is it a definition or is it somehow grounded in reality?
A continuous probability distribution can be interpreted as the prediction of rolling a fair dice with an infinite amount of sides, right? Then the probability of rolling each number would be zero, but still, every roll would show a number... an impossible event would have occurred, right?
Thank you all in advance!
Rolling a die is NOT a continuous probability distribution (CPD) but rather a discrete problem. For a CPD, it is impossible to get exactly an event. Imagine, the probability of a person being exactly 180 centimeters. It is almost impossible to be sure of that down to the atomic level. They can be 180.000000000...1 cms. But, we can be sure that they are between a certain range for instance between 179.99 and 180.01. This is not the case with the dice as they can only be one of 6 different events (1, 2, 3, 4, 5, 6). To summarise, continuous variables can only occur in a certain range. On the other hand, discrete variables, for example, rolling a die can occur as an exact event. I hope I was clear!
@@aayush5825 woah, perfect explanation. thanks!
@@aayush5825 great explanation
Thank you so much
10q for your brif explanation
something which doesn't make sense to me about the final point... if the probability of each single number occurring is 0, then how is the sum of all the numbers 1..
its very simple. Imagine that you are about to collect water from an ocean. The probability of getting a specific drop is close to almost zero(much similar to the limit theorem in calculus). But think about collecting say 10 litres, 100 litres or 1000 litres of water. You can see the probability increases. This is what I understood and it makes sense to me.
shouldn't it be a square at 6:53
kindly koe ye bta de k sta301 k paper ke kya tyari krnn k ye book pas ho jy koe abhi isi wkt bta de plzzzzz.mra sobo paper hain so plzzzzz
very great !
thank you, that was a great help...
Why isn't it 1/∞ ?
Great Help!
😭😭😭thank you for this video
Mr. Salman khan, u said de value can be any number from 1-5, so shudn't de probability b 1/infinity bcoz dere can be infinite numbers between 1 and 5
We're using the fact that the sum of the probability of all the events is 1. As we're dealing with a density function where the area under the curve is the probability of that function, we use the formula for the area of a rectangle and equate it to one.
You're getting confused between a PDF and a CDF. In a PDF the range of the function isn't bounded, the only condition that it has to follow is that the total probability is 1. Whereas for a cdf of a continuous random variable (as is the case here) the individual probability is 1/infinity, that is zero. Hope that this clears your doubt, else I'd strongly advice you to rewatch the video on what exactly is a pdf and what exactly is a cdf. Sal does an amazing job at this.
This guy is brilliant ... I just can't stand the fact he repeats himself so much. "Under the curve" ... "Under ... The cuuurve , Under the curve", I am always giggling to myself when he does that and he does that often. :/
so probability of 3 is 0
2 is also 0
1 is also 0
any no. is 0
and if we sum all probs we get that prob of 0 to 5 is 0 rather than 5*0.2 =1
You can't do that. There are infinite numbers from 0 to 5, which is why the probability of an exact number is 0. However, since the function is defined from 0 to 5, the probability of some number in this range is 100%. Does that make sense?
Thanks for the remarkable question and answer :D
@@GLu-tb1pbI'm not sure I understand. Lets say I randomly chose a number X between 1 and 5. Then I asked you what the probability of me randomly getting X. The probability of me getting exactly X is 0% yet somehow I still got X. The odds of getting X are 1/C as C approaches infinity. wouldn't the probability approach zero but never get there
@@gravity_well5627 oh, you're right. Because it's not actual infinity, it never becomes zero.
love u
i was doing this in school today
ngl he sounds hot i like his voice
what if you "roll the dice" and you do end up getting 3
not a cotinuous variable but a discrete
isn't the probability of getting three more like 1/∞
Gexco _ wouldn't that be 0
Interesting
jaldi bta de plzzzzzzzzzzzzz
His voice is somehow like Andrew Tate
3rd
As usual didnt explain the most importnat bit, why da hell probabulity of a exact value become zero, what is the explanation using probabilty, not using graphs?
+Amy Tan
Imagine you are weighing a piece of meat with a tool and the weight is equal = 1 KG.
If you want to treat this tool as the most perfect tool so the weighing process is no longer treated as a random event and you don't need the probability theory anymore.
But some one may say that the tool is just a normal tool and it's of course inaccurate by a certain degree.
Accordingly you'll assume that the real weight is = 1.X KG and since the tool is not too accurate it weighs only 1 KG.
1.X KG
What are possible values of x ? the answer is from 0 to 9
What is the probability for x to be = 0 ? the answer is 1/10.
What is the probability for that piece of meat to be equal 1.0 KG Exactly ? the answer is 1/(10^1)
Now, some other smart guy should ask you why you assumed that the real weight of that piece of meat was 1.X ? it is actually 1.XXXXXXXXXX KG (10 decimals) but your tool just read it 1 KG and neglected the other decimals.
1.XXXXXXXXXX KG (10 decimals)
What are possible values of x ? the answer is from 0 to 9
What is the probability for the 10'X'es to be = 0 at the same time ? the answer is 1/(10^10).
What is the probability for that piece of meat to be equal 1.000000000 KG Exactly ? the answer is 1/100000000000
So we can put in general mathematical form
P(Exact Number) = (1/10^a) ,
Where 'a' expresses to what extent you believe that there are more decimals existing than you can really measure.
Hope it helps
+Amy Tan
When you have 2 objects, the probability of getting one of them is 1/2. When you have 3 objects, the probability of getting one of them is 1/3.
Now here you have an infinite amount of objects, so the probability of having an exact value will be (1/n) with n going to infinity, the reciprocal of a very big number is one that gets closer and closer to zero, so at the end the reciprocal of a number going to infinity, will be zero. I hope this answered your question if something wasn't clear feel free to let me know.
luv 8
2nnndddd
1st view and 1st comment :)
ffs just take an integral it's not that big of a conceptual step lmao