a vase contains one red ball two white balls and three black balls. n balls are take out of the vase and (each ball returned to it afterwards). let B denote the number of black balls taken out and R denote the number of red balls taken out. what is the coefficient of correlation between R and B?(adsbygoogle = window.adsbygoogle || []).push({});

well i know that coeffieicnt of correlation = [itex]\frac{cov(R,B)}{\sigma R*\sigma B}[/itex]

and that R and B are simply bernouli trials with x and n-x trials respectivly.

my problem is calculating the covariance = E[RB] -E[R]E(E is the mean).

E[R] and Eare straightforward but E[RB] is a bit trickier for me.

i thought of using the definition of the mean with a multinomial vector for the shared probability for R and B and summing over 0<x<n, but is there an easier way?

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# Coefficient of correletion problem

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