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Lecture 4: Fix legend label #9

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Lecture 4: Fix legend label #9

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cfebb4c
Fix legend label
prparker Jan 24, 2026
e0c3b76
Remove warning text
prparker Jan 24, 2026
c3167e7
Fix warnings
prparker Jan 24, 2026
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76 changes: 5 additions & 71 deletions lecturebook/lecture04/hands-on-04.2.ipynb
View file
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Original file line number Diff line number Diff line change
Expand Up @@ -83,16 +83,6 @@
]
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"<>:6: SyntaxWarning: invalid escape sequence '\\p'\n",
"<>:6: SyntaxWarning: invalid escape sequence '\\p'\n",
"/var/folders/3n/r5vj11ss7lzcdl10vfhb_mw00000gs/T/ipykernel_68902/2154087378.py:6: SyntaxWarning: invalid escape sequence '\\p'\n",
" ax.set_ylabel(\"$\\phi(z)$\")\n"
]
},
{
"data": {
"image/svg+xml": [
Expand Down Expand Up @@ -727,7 +717,7 @@
"output_type": "display_data"
}
],
"source": "fig, ax = plt.subplots()\nimport numpy as np\nzs = np.linspace(-4.0, 4.0, 100)\nax.plot(zs, Z.pdf(zs))\nax.set_xlabel(\"$z$\")\nax.set_ylabel(\"$\\phi(z)$\")\nsns.despine(trim=True);"
"source": "fig, ax = plt.subplots()\nimport numpy as np\nzs = np.linspace(-4.0, 4.0, 100)\nax.plot(zs, Z.pdf(zs))\nax.set_xlabel(\"$z$\")\nax.set_ylabel(r\"$\\phi(z)$\")\nsns.despine(trim=True);"
},
{
"cell_type": "markdown",
Expand All @@ -749,16 +739,6 @@
]
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"<>:4: SyntaxWarning: invalid escape sequence '\\P'\n",
"<>:4: SyntaxWarning: invalid escape sequence '\\P'\n",
"/var/folders/3n/r5vj11ss7lzcdl10vfhb_mw00000gs/T/ipykernel_68902/625513495.py:4: SyntaxWarning: invalid escape sequence '\\P'\n",
" ax.set_ylabel(\"$\\Phi(z)$\")\n"
]
},
{
"data": {
"image/svg+xml": [
Expand Down Expand Up @@ -1396,7 +1376,7 @@
"output_type": "display_data"
}
],
"source": "fig, ax = plt.subplots()\nax.plot(zs, Z.cdf(zs))\nax.set_xlabel(\"$z$\")\nax.set_ylabel(\"$\\Phi(z)$\")\nsns.despine(trim=True);"
"source": "fig, ax = plt.subplots()\nax.plot(zs, Z.cdf(zs))\nax.set_xlabel(\"$z$\")\nax.set_ylabel(r\"$\\Phi(z)$\")\nsns.despine(trim=True);"
},
{
"cell_type": "markdown",
Expand Down Expand Up @@ -1600,24 +1580,6 @@
}
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"<>:5: SyntaxWarning: invalid escape sequence '\\p'\n",
"<>:6: SyntaxWarning: invalid escape sequence '\\m'\n",
"<>:8: SyntaxWarning: invalid escape sequence '\\p'\n",
"<>:5: SyntaxWarning: invalid escape sequence '\\p'\n",
"<>:6: SyntaxWarning: invalid escape sequence '\\m'\n",
"<>:8: SyntaxWarning: invalid escape sequence '\\p'\n",
"/var/folders/3n/r5vj11ss7lzcdl10vfhb_mw00000gs/T/ipykernel_68902/2312143129.py:5: SyntaxWarning: invalid escape sequence '\\p'\n",
" ax.plot(zs, Z.pdf(zs), label=\"$\\phi(x)$\")\n",
"/var/folders/3n/r5vj11ss7lzcdl10vfhb_mw00000gs/T/ipykernel_68902/2312143129.py:6: SyntaxWarning: invalid escape sequence '\\m'\n",
" ax.plot(zs, st.norm(loc=1.0).pdf(zs), label=\"$N(x|\\mu=1,\\sigma^2=1)$\")\n",
"/var/folders/3n/r5vj11ss7lzcdl10vfhb_mw00000gs/T/ipykernel_68902/2312143129.py:8: SyntaxWarning: invalid escape sequence '\\p'\n",
" ax.set_ylabel(\"$\\phi(x)$\")\n"
]
},
{
"data": {
"image/svg+xml": [
Expand Down Expand Up @@ -2997,7 +2959,7 @@
"output_type": "display_data"
}
],
"source": "# Plot the PDF of a standard normal and the PDF of a non-zero mean, unit variance normal\n# with an arrow indicating the change from the first to the second.\nfig, ax = plt.subplots()\nzs = np.linspace(-4.0, 4.0, 100)\nax.plot(zs, Z.pdf(zs), label=\"$\\phi(x)$\")\nax.plot(zs, st.norm(loc=1.0).pdf(zs), label=\"$N(x|\\mu=1,\\sigma^2=1)$\")\nax.set_xlabel(\"$x$\")\nax.set_ylabel(\"$\\phi(x)$\")\nax.legend(loc=\"best\", frameon=False)\nax.annotate(\"\", xytext=(0.0, 0.4), xy=(1.0, 0.4), arrowprops=dict(arrowstyle=\"->\",\n color=sns.color_palette()[2],\n lw=2))\nplt.title(\"The mean translates the standard normal PDF\")\nsns.despine(trim=True);\n"
"source": "# Plot the PDF of a standard normal and the PDF of a non-zero mean, unit variance normal\n# with an arrow indicating the change from the first to the second.\nfig, ax = plt.subplots()\nzs = np.linspace(-4.0, 4.0, 100)\nax.plot(zs, Z.pdf(zs), label=r\"$\\phi(x)$\")\nax.plot(zs, st.norm(loc=1.0).pdf(zs), label=r\"$N(x|\\mu=1,\\sigma^2=1)$\")\nax.set_xlabel(\"$x$\")\nax.set_ylabel(r\"$\\phi(x)$\")\nax.legend(loc=\"best\", frameon=False)\nax.annotate(\"\", xytext=(0.0, 0.4), xy=(1.0, 0.4), arrowprops=dict(arrowstyle=\"->\",\n color=sns.color_palette()[2],\n lw=2))\nplt.title(\"The mean translates the standard normal PDF\")\nsns.despine(trim=True);\n"
},
{
"cell_type": "markdown",
Expand All @@ -3016,20 +2978,6 @@
}
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"<>:4: SyntaxWarning: invalid escape sequence '\\p'\n",
"<>:5: SyntaxWarning: invalid escape sequence '\\m'\n",
"<>:4: SyntaxWarning: invalid escape sequence '\\p'\n",
"<>:5: SyntaxWarning: invalid escape sequence '\\m'\n",
"/var/folders/3n/r5vj11ss7lzcdl10vfhb_mw00000gs/T/ipykernel_68902/775679383.py:4: SyntaxWarning: invalid escape sequence '\\p'\n",
" ax.plot(zs, Z.pdf(zs), label=\"$\\phi(x)$\")\n",
"/var/folders/3n/r5vj11ss7lzcdl10vfhb_mw00000gs/T/ipykernel_68902/775679383.py:5: SyntaxWarning: invalid escape sequence '\\m'\n",
" ax.plot(zs, st.norm(loc=0.0, scale=np.sqrt(2.0)).pdf(zs), label=\"$N(x|\\mu=0,\\sigma^2=2)$\")\n"
]
},
{
"data": {
"image/svg+xml": [
Expand Down Expand Up @@ -4504,7 +4452,7 @@
"output_type": "display_data"
}
],
"source": "# Plot the PDF of a standard normal and the pdf of a zero mean Normal with variance two\nfig, ax = plt.subplots()\nzs = np.linspace(-4.0, 4.0, 100)\nax.plot(zs, Z.pdf(zs), label=\"$\\phi(x)$\")\nax.plot(zs, st.norm(loc=0.0, scale=np.sqrt(2.0)).pdf(zs), label=\"$N(x|\\mu=0,\\sigma^2=2)$\")\nax.set_xlabel(\"$x$\")\nax.set_ylabel(\"$p(x)$\")\nax.legend(loc=\"best\", frameon=False)\nplt.title(\"The variance scales the standard normal PDF\")\nsns.despine(trim=True);"
"source": "# Plot the PDF of a standard normal and the pdf of a zero mean Normal with variance two\nfig, ax = plt.subplots()\nzs = np.linspace(-4.0, 4.0, 100)\nax.plot(zs, Z.pdf(zs), label=r\"$\\phi(x)$\")\nax.plot(zs, st.norm(loc=0.0, scale=np.sqrt(2.0)).pdf(zs), label=r\"$N(x|\\mu=0,\\sigma^2=2)$\")\nax.set_xlabel(\"$x$\")\nax.set_ylabel(r\"$p(x)$\")\nax.legend(loc=\"best\", frameon=False)\nplt.title(\"The variance scales the standard normal PDF\")\nsns.despine(trim=True);"
},
{
"cell_type": "markdown",
Expand Down Expand Up @@ -5521,20 +5469,6 @@
}
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"<>:2: SyntaxWarning: invalid escape sequence '\\m'\n",
"<>:3: SyntaxWarning: invalid escape sequence '\\m'\n",
"<>:2: SyntaxWarning: invalid escape sequence '\\m'\n",
"<>:3: SyntaxWarning: invalid escape sequence '\\m'\n",
"/var/folders/3n/r5vj11ss7lzcdl10vfhb_mw00000gs/T/ipykernel_68902/1046293625.py:2: SyntaxWarning: invalid escape sequence '\\m'\n",
" ax.hist(x_samples, density=True, alpha=0.5, label=\"Samples from $X = \\mu + \\sigma Z$\")\n",
"/var/folders/3n/r5vj11ss7lzcdl10vfhb_mw00000gs/T/ipykernel_68902/1046293625.py:3: SyntaxWarning: invalid escape sequence '\\m'\n",
" ax.plot(xs, X.pdf(xs), label=\"PDF of $N(\\mu, \\sigma^2)$\")\n"
]
},
{
"data": {
"image/svg+xml": [
Expand Down Expand Up @@ -6884,7 +6818,7 @@
"output_type": "display_data"
}
],
"source": "fig, ax = plt.subplots()\nax.hist(x_samples, density=True, alpha=0.5, label=\"Samples from $X = \\mu + \\sigma Z$\")\nax.plot(xs, X.pdf(xs), label=\"PDF of $N(\\mu, \\sigma^2)$\")\nax.set_xlabel(\"$x$\")\nax.set_ylabel(\"$p(x)$\")\nplt.legend(loc=\"best\", frameon=False)\nsns.despine(trim=True);"
"source": "fig, ax = plt.subplots()\nax.hist(x_samples, density=True, alpha=0.5, label=r\"Samples from $X = \\mu + \\sigma Z$\")\nax.plot(xs, X.pdf(xs), label=r\"PDF of $N(\\mu, \\sigma^2)$\")\nax.set_xlabel(\"$x$\")\nax.set_ylabel(\"$p(x)$\")\nplt.legend(loc=\"best\", frameon=False)\nsns.despine(trim=True);"
},
{
"cell_type": "markdown",
Expand Down
17 changes: 5 additions & 12 deletions lecturebook/lecture04/reading-04.ipynb
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Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -3481,19 +3481,12 @@
"iopub.status.busy": "2025-06-16T15:03:23.011568Z",
"iopub.status.idle": "2025-06-16T15:03:23.125520Z",
"shell.execute_reply": "2025-06-16T15:03:23.125261Z"
}
},
"tags": [
"hide-input"
]
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"<>:7: SyntaxWarning: invalid escape sequence '\\m'\n",
"<>:7: SyntaxWarning: invalid escape sequence '\\m'\n",
"/var/folders/3n/r5vj11ss7lzcdl10vfhb_mw00000gs/T/ipykernel_68920/3227439545.py:7: SyntaxWarning: invalid escape sequence '\\m'\n",
" plt.axvline(x=0, color='r', linestyle='--', label='$\\mathbb{E}[X]$')\n"
]
},
{
"data": {
"image/svg+xml": [
Expand Down Expand Up @@ -4815,7 +4808,7 @@
"output_type": "display_data"
}
],
"source": "# Plot the pdf of a mixture of two normal random variables with different means but the same variance\nfrom scipy.stats import norm\nx = np.linspace(-10, 10, 200)\ny = 0.5 * norm.pdf(x, loc=-5) + 0.5 * norm.pdf(x, loc=5)\nplt.plot(x, y)\n# Add the expected value\nplt.axvline(x=0, color='r', linestyle='--', label='$\\mathbb{E}[X]$')\nplt.xlabel('$x$')\nplt.ylabel('$f_X(x)$')\nsns.despine(trim=True)\nplt.title(\"Example of a case in which the expected value is not representative of the distribution\");"
"source": "# Plot the pdf of a mixture of two normal random variables with different means but the same variance\nfrom scipy.stats import norm\nx = np.linspace(-10, 10, 200)\ny = 0.5 * norm.pdf(x, loc=-5) + 0.5 * norm.pdf(x, loc=5)\nplt.plot(x, y)\n# Add the expected value\nplt.axvline(x=0, color='r', linestyle='--', label=r'$\\mathbb{E}[X]$')\nplt.legend()\nplt.xlabel('$x$')\nplt.ylabel('$f_X(x)$')\nsns.despine(trim=True)\nplt.title(\"Example of a case in which the expected value is not representative of the distribution\");"
},
{
"cell_type": "markdown",
Expand Down