# Problem 3.8 Cyclic SCMs

## a) SCM with Unique Solution

Given SCM
\begin{align}
X:=&2Y+N_X\\
Y:=&2X+N_Y
\end{align}
and the substituted equations
\begin{align}
X:=&\alpha N_X+\beta N_Y\\
Y:=&\gamma N_X+\delta N_Y
\end{align}
compute a solution $(\alpha,\beta,\gamma,\delta)$ that satisfies the equations.

### Solution

The solution can be found by solving the linear system of equations which yields
\begin{align}
X=&-\frac{1}{3}N_X-\frac{2}{3}N_Y\\
Y=&-\frac{1}{3}N_Y-\frac{2}{3}N_X
\end{align}

Corresponding to the solution 
$$
(\alpha,\beta,\gamma,\delta)=
-\left(\frac{1}{3},\frac{2}{3},\frac{2}{3},\frac{1}{3}\right)
$$

## b) SCM with Potential Solution


```python

```

7657e2b2862f2fec845b560ec0616be2b015fa8e
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Jupyter Notebook
causal-inference/problems/problem-3.8-cyclic-scms.ipynb
Simsso/Machine-Learning-Tinkering
0a024aab0bb1ac5fbdd2f77380ab36d192278701
MIT
2020-02-19T16:30:04.000Z
2020-03-13T02:22:29.000Z
causal-inference/problems/problem-3.8-cyclic-scms.ipynb
Simsso/Machine-Learning-Tinkering
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MIT
2021-02-17T14:00:33.000Z
2022-02-10T03:05:35.000Z
causal-inference/problems/problem-3.8-cyclic-scms.ipynb
Simsso/Machine-Learning-Tinkering
0a024aab0bb1ac5fbdd2f77380ab36d192278701
MIT
Qwen/Qwen-72B
1. YES
2. YES