Dear Statisticians and Mathematicians,
I am interested in proving the following lemma by induction
I have shown that it holds true for $n=2$ which I don't provide its proof here. We assume it is true when $n$ is replaced by $n-1$. I conditioned on $Y_1+...+Y_{n-1}$ but I could not prove. I don't know how to use the induction hypothesis to prove the lemma. I really appreciate any help of you guys in this regard.