S3 chapter 3 confusion Watch

Angels1234
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Can someone explain what the difference is between xbar and Xbar ?? Doing central limit theorem and I’m getting confused : S
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Shaanv
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Could u post a picture of what you are referring to?
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old_engineer
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(Original post by Angels1234)
Can someone explain what the difference is between xbar and Xbar ?? Doing central limit theorem and I’m getting confused : S
In my understanding, Xbar denotes the mean of a sample of X values in general, while xbar denotes the value of an individual sample mean.
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Angels1234
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(Original post by old_engineer)
In my understanding, Xbar denotes the mean of a sample of X values in general, while xbar denotes the value of an individual sample mean.
When you say in general do you mean for an entire population rather than a sample
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old_engineer
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(Original post by Angels1234)
When you say in general do you mean for an entire population rather than a sample
I meant “in general for a sample” rather than anything about the entire population.

If you are happy with the distinction between X and x, then the same distinction applies between Xbar and xbar.
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Angels1234
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(Original post by old_engineer)
I meant “in general for a sample” rather than anything about the entire population.

If you are happy with the distinction between X and x, then the same distinction applies between Xbar and xbar.
I’m not sure if I get it still
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RDKGames
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Not an expert and may get corrected, but consider the difference between X and x. We say X is a random variable, while x is not. We use them in notation like P(X=x) where it reads 'the probability that X is equal to x'.

Same thing applies to \bar{X} and \bar{x}. We denote \bar{X} as the random variable while \bar{x} is not a random variable. Similarly, we may use it in the context of P(\bar{X} = \bar{x}) where we take a bunch of samples out of our population X, take all of their means and assign a r.v. to them which is \bar{X}, then we look at the probability that it equals a particular sample mean \bar{x}.
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old_engineer
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(Original post by Angels1234)
I’m not sure if I get it still
Let’s say X is a random variable that represents the heights of maths students. X will have an expected value, variance and distribution of some kind. x then represents the height of an individual maths student (x is an individual value of X). Hence statements like P(X < x) = 0.7 make sense.

Now let’s say we take several idependent samples of 20 students from the population of maths students. The mean height calculated for these samples can be represented by the random variable Xbar. Xbar will have an expected value, variance and distribution of some kind. xbar is the mean calculated for any individual sample. Hence statements like P(Xbar < xbar) = 0.7 make sense.
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Angels1234
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(Original post by RDKGames)
Not an expert and may get corrected, but consider the difference between X and x. We say X is a random variable, while x is not. We use them in notation like P(X=x) where it reads 'the probability that X is equal to x'.

Same thing applies to \bar{X} and \bar{x}. We denote \bar{X} as the random variable while \bar{x} is not a random variable. Similarly, we may use it in the context of P(\bar{X} = \bar{x}) where we take a bunch of samples out of our population X, take all of their means and assign a r.v. to them which is \bar{X}, then we look at the probability that it equals a particular sample mean \bar{x}.
ahh okay. So basically xbar is just the sample mean of one sample where as XBar is a random variable (more generic) as it involves looking at several different samples , where each sample has its own sample mean and X bar is the rv of getting lets say the mean of one sample or the mean of another sample ?
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Angels1234
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(Original post by old_engineer)
Let’s say X is a random variable that represents the heights of maths students. X will have an expected value, variance and distribution of some kind. x then represents the height of an individual maths student (x is an individual value of X). Hence statements like P(X < x) = 0.7 make sense.

Now let’s say we take several idependent samples of 20 students from the population of maths students. The mean height calculated for these samples can be represented by the random variable Xbar. Xbar will have an expected value, variance and distribution of some kind. xbar is the mean calculated for any individual sample. Hence statements like P(Xbar < xbar) = 0.7 make sense.
okay so X bar is a rv that represents what the mean could be from a sample . so if there is 5 samples of 20 people for instance and 1 of those samples has a mean of lets say 1.67 m then the Rv Xbar would take / equal this value and then if another sample has a mean of 1.64 Xbar can allso take this value ?
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RDKGames
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(Original post by Angels1234)
ahh okay. So basically xbar is just the sample mean of one sample where as XBar is a random variable (more generic) as it involves looking at several different samples , where each sample has its own sample mean and X bar is the rv of getting lets say the mean of one sample or the mean of another sample ?
Pretty much.
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Angels1234
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(Original post by RDKGames)
Pretty much.
Fabulous . Thanks for clearing it up
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old_engineer
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(Original post by Angels1234)
okay so X bar is a rv that represents what the mean could be from a sample . so if there is 5 samples of 20 people for instance and 1 of those samples has a mean of lets say 1.67 m then the Rv Xbar would take / equal this value and then if another sample has a mean of 1.64 Xbar can allso take this value ?
Yes.
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