🌐 [translation-sync] [perm_income.md] Update np.random → Generator API (#199)

* Update translation: lectures/perm_income.md

* Update translation: .translate/state/perm_income.md.yml

Author: mmcky

.translate/state/perm_income.md.yml

@@ -1,6 +1,6 @@
-source-sha: a73ba0f7db0a6783ab5b9cca269a9f95f88106cb
-synced-at: "2025-06-17"
-model: unknown
-mode: RESYNC
+source-sha: ab687aad2134b4eee2835f896be4b956e73001bb
+synced-at: "2026-07-23"
+model: claude-sonnet-5
+mode: UPDATE
 section-count: 6
-tool-version: 0.20.0
+tool-version: 0.22.0

lectures/perm_income.md

@@ -501,8 +501,8 @@ r = 0.05
 T = 60
 
 @jit
-def time_path(T):
-    w = np.random.randn(T+1)  # w_0, w_1, ..., w_T
+def time_path(T, rng):
+    w = rng.standard_normal(T+1)  # w_0, w_1, ..., w_T
     w[0] = 0
     b = np.zeros(T+1)
     for t in range(1, T+1):
@@ -511,7 +511,8 @@ def time_path(T):
     c = μ + (1 - β) * (σ * w - b)
     return w, b, c
 
-w, b, c = time_path(T)
+rng = np.random.default_rng()
+w, b, c = time_path(T, rng)
 
 fig, ax = plt.subplots(figsize=(10, 6))
 
@@ -534,7 +535,7 @@ fig, ax = plt.subplots(figsize=(10, 6))
 
 b_sum = np.zeros(T+1)
 for i in range(250):
-    w, b, c = time_path(T)  # Generate new time path
+    w, b, c = time_path(T, rng)  # Generate new time path
     rcolor = random.choice(('c', 'g', 'b', 'k'))
     ax.plot(c, color=rcolor, lw=0.8, alpha=0.7)
 
@@ -1025,4 +1026,3 @@ $$
 [^f5]: 如果由$y^t$张成的线性空间等于由$w^t$张成的线性空间，则过程$y_t$的移动平均表示被称为**基本的**。通过卡尔曼滤波获得的时不变创新表示在构造上是基本的。
 
 [^f8]: 相关思想的有趣应用请参见{cite}`CampbellShiller88`、{cite}`LettLud2001`、{cite}`LettLud2004`。
-