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 IlanSherer March 29th, 2018 06:24 PM

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!

 romsek March 30th, 2018 09:08 AM

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.

 IlanSherer March 30th, 2018 09:57 AM

Quote:
 Originally Posted by romsek (Post 591040) 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.

 romsek March 30th, 2018 10:11 AM

Quote:
 Originally Posted by IlanSherer (Post 591044) 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.

 IlanSherer March 30th, 2018 10:25 AM

Quote:
 Originally Posted by romsek (Post 591045) 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?

 romsek March 30th, 2018 01:37 PM

Quote:
 Originally Posted by IlanSherer (Post 591046) 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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