Can anyone help me to solve the exercise $(4.6.9)$ from Nitis Mukhopadyay book ? I do not know even how to begin the transformation technique suggested. I'm interested in the derivation of $(11.4.11)$ from this question.
EDIT: There are 2 snippets under this question : page 238 showing exercise 4.6.9. which I would like to see solved. On the second snippets is the definition of Pearson correlation coefficient $r$ in 4.6.7. My problem is dated back to the beginning of the exercise 4.6.9. which I'm unable even to start solving.
where $r$ is given by $(4.3.7)$
SECOND SNIPPET
EDIT 2
I've obtained (please see the 3rd snippet below) the required solution but for the fact that I've obtained an extra factor $\frac{1}{(n-2)}$ please see the very last circled question mark there. as opposed to Wanted [=Chceme in Czech].
Dictionary for you to my manuscript: Chceme=Wanted Vzorec=Formula Obecne=In general
Could you please point me to the place at which I must have an error ?
There is an error in the second to last line. The exponent of $n-2$ should be $-\frac 12$, i.e. $(n-2)^{-\frac 12}$ because there is already a factor of $n-2$ in the third to last line, therefore you should not multiply by $(n-2)^{\frac 32}(n-2)^{-\frac 32}$ but $(n-2)^{\frac 12}(n-2)^{-\frac 12}$. To povede k odpovědi.