diff options
Diffstat (limited to 'houdre')
| -rw-r--r-- | houdre/01_foundations | 1 | ||||
| -rw-r--r-- | houdre/hw1.tex | 2 |
2 files changed, 1 insertions, 2 deletions
diff --git a/houdre/01_foundations b/houdre/01_foundations index aedcdd2..b703fa3 100644 --- a/houdre/01_foundations +++ b/houdre/01_foundations @@ -18,7 +18,6 @@ Cardinality of empty set is 0. (why is this a convention and not a self-evident fact?) Card S = #S = cardinality of S - Flip a coin until first tail, and stop. Count # of flips. Omega = {1,2,3,...} = Natural numbers. (Sometimes also {0,1,2,...}) Card N = +\infty diff --git a/houdre/hw1.tex b/houdre/hw1.tex index c06f5fa..e49bd49 100644 --- a/houdre/hw1.tex +++ b/houdre/hw1.tex @@ -144,7 +144,7 @@ $$\Pr(A\cup B) = \Pr(A\setminus B)+\Pr(B\setminus A)+\Pr(A\cap B)$$ $$= (\Pr(A\setminus B)+\Pr(A\cap B)) + (\Pr(B\setminus A)+\Pr(A\cap B)) - \Pr(A\cap B)$$ $$= \Pr(A) + \Pr(B) - \Pr(A\cap B) -= \sum_i \Pr(A_i) - \sum_{i<j} \Pr(A_i\cap A_j).$$ += \sum_i \Pr(A_i) - \sum_{i<j} \Pr(A_i\cap A_j).$$ Let the above be considered a base case, with the successive case $U_n = U_{n-1}\cup A_n.$ |