correlation coefficient

[zhenyazh]

hi
another exam preparation question:
let x1..xn be random varibale independent and with same dist.
they have exp. u and variance v.
let m be a natural number so that n>m>1/2*n
y=sum of xi 1 until m
z=sum of xi n+1-m until n
what is the correlation coefficient between y and z.
i think i know how to do it but i get a result that i don't have in answers options.
as far as i understand i should count how many common xi's are there between y and z, because in counting the corr. coeff. only they count. their combination with others results on cov=0. as soon as i know that i can easily calculate. but i guess i am wrong in finding their number.
can you help?

thanks

[BGM]

As long as they are independent, they have 0 correlation?

[zhenyazh]

yes. if they are indpndnt they are also uncorrelated. thus cov=0