We assume that, for all $k\in\mathbb{N}$, $p_k=\frac{1}{2^{k+1}}$. We have $\varphi_n(t)=\frac{n+(1-n)t}{1+n-nt}$. Express, for $(n,k)\in\mathbb{N}^2$, $P(Y_n=k)$ in terms of $n$ and $k$.
We assume that, for all $k\in\mathbb{N}$, $p_k=\frac{1}{2^{k+1}}$. We have $\varphi_n(t)=\frac{n+(1-n)t}{1+n-nt}$.
Express, for $(n,k)\in\mathbb{N}^2$, $P(Y_n=k)$ in terms of $n$ and $k$.