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March 29th, 2018, 07:24 PM   #1
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Statistics

Hello

Can you help me please about the next exercise:

For 25 students, math scores and physics scores were recorded, the average of the two exams was identical, which is 75, and the standard deviation of the two exams was identical too, which is 12.
What is the value of pearson correlation coefficient? (if it exists).

I tried to find it, but I did not succeed.
In my opinion - it doesn't exist, because I don't have enough data from the question.
I'm not sure, it's just my opinion, maybe I'm missing something.

Thanks!
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March 30th, 2018, 10:08 AM   #2
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You aren't told, and there is no way of determining, whether the two scores are independent.

If they are independent the correlation coefficient is zero as

$E[P M] = E[P]E[M]$

Without having you hands on the joint distribution in some form you can't compute the correlation.
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March 30th, 2018, 10:57 AM   #3
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Quote:
Originally Posted by romsek View Post
You aren't told, and there is no way of determining, whether the two scores are independent.

If they are independent the correlation coefficient is zero as

$E[P M] = E[P]E[M]$

Without having you hands on the joint distribution in some form you can't compute the correlation.
I'm sorry, but what do you mean "independent"?
I understood the word, but i didn't understand what did you mean.
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March 30th, 2018, 11:11 AM   #4
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Quote:
Originally Posted by IlanSherer View Post
I'm sorry, but what do you mean "independent"?
I understood the word, but i didn't understand what did you mean.
You have studied probability to the point that you are computing correlation coefficients but you don't know what it is for two random variables to be statistically independent?

I don't know how this is possible.

Revisit your text. Independence of random variables is a fundamental concept.
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March 30th, 2018, 11:25 AM   #5
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Quote:
Originally Posted by romsek View Post
You have studied probability to the point that you are computing correlation coefficients but you don't know what it is for two random variables to be statistically independent?

I don't know how this is possible.

Revisit your text. Independence of random variables is a fundamental concept.
Oh sorry, yes they are independent.
But why the answer is 0?
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March 30th, 2018, 02:37 PM   #6
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Quote:
Originally Posted by IlanSherer View Post
Oh sorry, yes they are independent.
But why the answer is 0?
$\rho = \dfrac{E[MP]-E[M]E[P]}{\sigma_M \sigma_P} = 0$

when

$E[MP]=E[M]E[P]$
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