One-step Binomial model's Radon-Nikodym derivative

In the one-step binomial model…

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Question 1: What exactly is a ‘$frac{d mathbb Q}{d mathbb P}$‘?

I think it’s $frac{d mathbb Q}{d mathbb P} = frac{q_u}{p_u}1_u + frac{q_d}{p_d}1_d$, so it’s some asset with payoffs $frac{q_u}{p_u}$ and $frac{q_d}{p_d}$, expected value of 1 and replicating portfolio $(x,y)$ of

$$x=frac{1}{1+R}frac{u(frac{q_d}{p_d})-d(frac{q_u}{p_u})}{u-d}$$
$$y=frac{1}{S_0}frac{frac{q_u}{p_u}-frac{q_d}{p_d}}{u-d}$$

This seems to be some replicating portfolio that is expected to payoff 1 at $t=1$.

Well, $(x,y)=(frac{1}{1+R},0)$ seems to give the same payoff but with -100% lower risk

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Question 2: What exactly is a/an ‘$Xfrac{d mathbb Q}{d mathbb P}$‘?

We could say that the price of X uses not

$$E[X] = X_up_u+X_dp_d$$

but rather

$$E^{mathbb Q}[X] = E[Xfrac{d mathbb Q}{d mathbb P}] = X_ufrac{q_u}{p_u}p_u + frac{q_d}{p_d}p_d$$

I guess it’s some asset that pays $X_ufrac{q_u}{p_u}$ or $X_dfrac{q_d}{p_d}$ then replicating portfolio is…then idk. Not sure we need one since we’re using real world probabilities anyhoo