diff --git a/reading/000_Introduction to Probability, Statistics, and Random Processes/ch1/notes.ipynb b/reading/000_Introduction to Probability, Statistics, and Random Processes/ch1/notes.ipynb index 6a23af0..4e86bc1 100644 --- a/reading/000_Introduction to Probability, Statistics, and Random Processes/ch1/notes.ipynb +++ b/reading/000_Introduction to Probability, Statistics, and Random Processes/ch1/notes.ipynb @@ -55,7 +55,14 @@ "$n = 3$ case:\n", "\n", "$|A \\cup B \\cup C| = |A| + |B| + |C| - |A \\cap B| - |A \\cap C| - |B \\cap C| + |A \\cap B \\cap C|$\n", - "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "id": "c7475d4f", + "metadata": {}, + "source": [ "## Random experiments (1.3.1 - 1.4)\n", "\n", "- A **random experiment** is a process by which we observe something uncertain\n", @@ -80,13 +87,25 @@ "\n", "\\begin{align*}\n", "P(A) = \\frac{|A|}{|S|}\n", - "\\end{align*}\n", - "\n", + "\\end{align*}" + ] + }, + { + "cell_type": "markdown", + "id": "b705ef32", + "metadata": {}, + "source": [ "## Conditional probability (1.4.0)\n", "\n", "If $A$ and $B$ are twos events in sample space $S$, then the **conditional probability of $A$ given $B$** is defined as\n", "\n", "\\begin{align*}\n", + "P(A|B) = \\frac{P(A \\cap B)}{P(B)}, \\text{when } P(B) > 0\n", + "\\end{align*}\n", + "\n", + "or\n", + "\n", + "\\begin{align*}\n", "P(A|B) = \\frac{|A \\cap B|}{|B|}, \\text{when } P(B) > 0\n", "\\end{align*}\n", "\n",