math121b:04-15
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math121b:04-15 [2020/04/14 22:52] pzhou [How to play the probability game?] |
math121b:04-15 [2020/04/15 09:44] (current) pzhou |
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| ** Conditional Probability **: suppose we want to know "given that $A$ happens, what is the probability $B$ will happen?" | ** Conditional Probability **: suppose we want to know "given that $A$ happens, what is the probability $B$ will happen?" | ||
| - | $$ \P(A | B) := \frac{ \P(A \cap B) } {\P(B) | + | $$ \P(A | B) := \frac{ \P(A \cap B) } {\P(B) } $$ |
| ** The product rule ** | ** The product rule ** | ||
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| ===== How to play the probability game? ===== | ===== How to play the probability game? ===== | ||
| First thing first, find out what is $\Omega$ and $\P$. | First thing first, find out what is $\Omega$ and $\P$. | ||
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| + | Be aware when someone say: "let me randomly choose ...." | ||
| Here is an interesting example: [[https:// | Here is an interesting example: [[https:// | ||
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| + | Another hard example: let $M$ be a random symmetric matrix of size $N \times N$, where each entry is iid Gausian. Question: how does eigenvalues of this matrix distribute? | ||
math121b/04-15.1586929921.txt.gz · Last modified: 2020/04/14 22:52 by pzhou
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