Im so confused. If Xi is a random variable, then how can you compare their orders?how do you know which one is bigger since random variable is not a single value?I'm so confused plz help.
Crazy to me how this is the only video on this topic in English. You explained it well but is this topic irrelevant in statistics or why has literally no one else made a vide on this in 8 years.
I don't understand why Xsub(1) and Xsub(2) are not independent, all you did was rearrange the observations in ascending order, and why do we write Xsub1, Xsub2 (with no parentheses on the subscripts) in capital letters if they're all the same variable: the time it takes to finish a race around a track? Why isn't there just one variable, X: the time it takes to finish a race around a track, and that X can take values x1, x2, x3,..., xn?
+Yelmy So let me address your last question first... Suppose you do just have one random variable called X, and suppose it will take on a value from the set {x1, x2, ..., xn}. In this case X is a discrete random variable, btw. Now suppose that random variable X models the number of my children who are sick (could be 0, or 1, or 2, ... any value from the set {0, 1, 2, ..., 22} (yes, I have 22 children)... the x1=0, x2=1, ..., x23=22. That's okay, right? But what if I want to track the number of my children who are sick each day for the next 10 days? Then I actually need 10 random variables- one for each day. So maybe X1 = # of sick kids on day 1; X2 = # of sick kids on day 2, ..., X10 = # of sick kids on day 10. Maybe each one of these random variables has the same distribution, meaning any one of them, say, Xi takes on a value from the set {0, 1, ..., 22} according to the same set of probabilities. So it makes sense that you might need more than one random variable, right? Now, these ten random variables could be highly dependent or totally independent I think, depending on whether or not my 22 children all live at home... or if they all live in different places around the world. Finally, what about the Xsub(1), Xsub(2)? So Xsub(1) is the minimum of those ten random variables X1, X2, ..., X10, which is also a random variable! See, it could be that those ten random variables X1, X2, ... take on the values 2, 3, 2, 6, 5, 5, 4, 3, 6, 8 ...and in that order. In this case Xsub(1) takes the value 2. Or, it might be that those ten random variables take on the values 3, 4, 5, 6, 5, 7, 8, 9, 7, 6 ...and in that order. In this case Xsub(1) takes the value 3. Or, it might be that those ten random variables take the values 8, 6, 8, 6, 8, 7, 7, 5, 6, 12 ... and in that order. In this case, Xsub(1) takes the value 5. So you see the minimum of those ten random variables is also a random variable. In the example from the video I think I mentioned race times. Well, you could think of the same runner running 400 meters as fast as possible each day for ten days. Maybe those race times are independent continuous random variables from the same distribution. With probability 1, one of those ten race times will be the best (minimum) and one will be the worst (maximum). Both the minimum and maximum will be random variables.
+Matthew Jones Thank you so much for taking the time to explain that. I do understand that Xsub(1) and Xsub(2) are random variables, but what I don't get is why they're not considered independent, you briefly mention that they're not independent at the start of this video, I don't get why the rearrangement of my observations (or realisations) doesn't make them independent anymore, even though I randomly selected my elements and recorded their values/the observations/realisations...
Oh, okay. I misunderstood. Let's think about a really simple scenario- you have two people running from a bear in the woods. Person 1 will take X_1 seconds to get back to camp and person 2 will take X_2 seconds to get back to camp, and both of these times are random variables that are independent with the same distribution. However, Xsub(1) is always less than or equal to Xsub(2), right? So given you know the value of Xsub(1), this information changes what values Xsub(2) can take on. For example, if Xsub(1) turns out to be 1 second, then the second person to finish (might be person 1, might be person 2) might still have a good chance of outrunning the bear. However, if you know that Xsub(1) is at least 10,000,000 seconds, then it's very likely the second person to finish is bear food. In general, Xsub(i) is alwals less than or equal to Xsub(i+1), and so the set of them will be neither pairwise nor mutually independent.
Thank you Order statistics Guru. This is the best video I found on UA-cam on the subject.
Thanks for the video! Really appreciate you posting this material
Dude, you explained it clearly and the concept is now crystal clear to me. Definitely, thumbs up 👍 Thank you!
Can you place the probability into a playlist.
Great job! Thank you very much
Thank you so much Matthew!!!
Easy to understand and well explained, thanks a lot....!!!
Thank you :)
Thank you so much,clear and concise :)
Great video super helpful!
Im so confused. If Xi is a random variable, then how can you compare their orders?how do you know which one is bigger since random variable is not a single value?I'm so confused plz help.
very, very clear and helpful video. thank you
thats so clear. i love it
It is wonderful. But, bro please write it a little bit worse because we can still read it.. :)
thx! very clear, helps a lot
very helpful! thank you!
Crazy to me how this is the only video on this topic in English. You explained it well but is this topic irrelevant in statistics or why has literally no one else made a vide on this in 8 years.
Thank you, this was really useful
Thank you!
Dankeschön.
I don't understand why Xsub(1) and Xsub(2) are not independent, all you did was rearrange the observations in ascending order, and why do we write Xsub1, Xsub2 (with no parentheses on the subscripts) in capital letters if they're all the same variable: the time it takes to finish a race around a track?
Why isn't there just one variable, X: the time it takes to finish a race around a track, and that X can take values x1, x2, x3,..., xn?
+Yelmy So let me address your last question first... Suppose you do just have one random variable called X, and suppose it will take on a value from the set {x1, x2, ..., xn}. In this case X is a discrete random variable, btw. Now suppose that random variable X models the number of my children who are sick (could be 0, or 1, or 2, ... any value from the set {0, 1, 2, ..., 22} (yes, I have 22 children)... the x1=0, x2=1, ..., x23=22. That's okay, right?
But what if I want to track the number of my children who are sick each day for the next 10 days? Then I actually need 10 random variables- one for each day. So maybe X1 = # of sick kids on day 1; X2 = # of sick kids on day 2, ..., X10 = # of sick kids on day 10. Maybe each one of these random variables has the same distribution, meaning any one of them, say, Xi takes on a value from the set {0, 1, ..., 22} according to the same set of probabilities. So it makes sense that you might need more than one random variable, right? Now, these ten random variables could be highly dependent or totally independent I think, depending on whether or not my 22 children all live at home... or if they all live in different places around the world.
Finally, what about the Xsub(1), Xsub(2)? So Xsub(1) is the minimum of those ten random variables X1, X2, ..., X10, which is also a random variable! See, it could be that those ten random variables X1, X2, ... take on the values
2, 3, 2, 6, 5, 5, 4, 3, 6, 8
...and in that order. In this case Xsub(1) takes the value 2. Or, it might be that those ten random variables take on the values
3, 4, 5, 6, 5, 7, 8, 9, 7, 6
...and in that order. In this case Xsub(1) takes the value 3. Or, it might be that those ten random variables take the values
8, 6, 8, 6, 8, 7, 7, 5, 6, 12
... and in that order. In this case, Xsub(1) takes the value 5.
So you see the minimum of those ten random variables is also a random variable.
In the example from the video I think I mentioned race times. Well, you could think of the same runner running 400 meters as fast as possible each day for ten days. Maybe those race times are independent continuous random variables from the same distribution. With probability 1, one of those ten race times will be the best (minimum) and one will be the worst (maximum). Both the minimum and maximum will be random variables.
+Matthew Jones Thank you so much for taking the time to explain that.
I do understand that Xsub(1) and Xsub(2) are random variables, but what I don't get is why they're not considered independent, you briefly mention that they're not independent at the start of this video, I don't get why the rearrangement of my observations (or realisations) doesn't make them independent anymore, even though I randomly selected my elements and recorded their values/the observations/realisations...
Oh, okay. I misunderstood. Let's think about a really simple scenario- you have two people running from a bear in the woods. Person 1 will take X_1 seconds to get back to camp and person 2 will take X_2 seconds to get back to camp, and both of these times are random variables that are independent with the same distribution. However, Xsub(1) is always less than or equal to Xsub(2), right? So given you know the value of Xsub(1), this information changes what values Xsub(2) can take on. For example, if Xsub(1) turns out to be 1 second, then the second person to finish (might be person 1, might be person 2) might still have a good chance of outrunning the bear. However, if you know that Xsub(1) is at least 10,000,000 seconds, then it's very likely the second person to finish is bear food.
In general, Xsub(i) is alwals less than or equal to Xsub(i+1), and so the set of them will be neither pairwise nor mutually independent.