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![Page 1: Brain Teaser Two jars contain the same total numbers of balls, some blacks and some whites in each. From each urn are drawn n balls with replacement, where.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649de65503460f94ade869/html5/thumbnails/1.jpg)
Brain Teaser
• Two jars contain the same total numbers of balls, some blacks and some whites in each. From each urn are drawn n balls with replacement, where n >= 3.
• Find the number of drawings and the composition of the two urns so that the probability that all white balls are drawn from the first urn is equal to the probability that the drawing from the second is either all whites or all blacks.
Question
![Page 2: Brain Teaser Two jars contain the same total numbers of balls, some blacks and some whites in each. From each urn are drawn n balls with replacement, where.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649de65503460f94ade869/html5/thumbnails/2.jpg)
Brain Teaser
• Let x be the number of whites in the first, y be the number of whites in the second, and z be the number of blacks in the second.
• +• Look familiar?– Fermat’s Last Theorem: Impossible for n >=3
Answer
![Page 3: Brain Teaser Two jars contain the same total numbers of balls, some blacks and some whites in each. From each urn are drawn n balls with replacement, where.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649de65503460f94ade869/html5/thumbnails/3.jpg)
Market Update
• Obamacare now in full-on derp mode• EU Q2’2013 GDP: +0.1% (after +0.3% in
Q2’2013)• Yellen testimony lives up to her reputation• Empire state mfg: -2.2 (exp. 5)• Japanese growth story continues
Week in Review
![Page 4: Brain Teaser Two jars contain the same total numbers of balls, some blacks and some whites in each. From each urn are drawn n balls with replacement, where.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649de65503460f94ade869/html5/thumbnails/4.jpg)
Quantitative Finance SocietyThe Great Recession vs. The Great Depression
![Page 5: Brain Teaser Two jars contain the same total numbers of balls, some blacks and some whites in each. From each urn are drawn n balls with replacement, where.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649de65503460f94ade869/html5/thumbnails/5.jpg)
Background
• Great Depression– World War I cements
US– Crash of 1920 brings
roaring twenties– Shallow recessions in
1923 and 1927– “Bucket shops”– Gold standard
![Page 6: Brain Teaser Two jars contain the same total numbers of balls, some blacks and some whites in each. From each urn are drawn n balls with replacement, where.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649de65503460f94ade869/html5/thumbnails/6.jpg)
Background
• Great Recession– Financial de-
regulation– Rise of the 401(k)– “Goldilocks
economy”– Housing boom– Shadow banking
and risk concentration
![Page 7: Brain Teaser Two jars contain the same total numbers of balls, some blacks and some whites in each. From each urn are drawn n balls with replacement, where.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649de65503460f94ade869/html5/thumbnails/7.jpg)
During the crisis
• Great Depression– Dust Bowl– Black Tuesday: Crash of
1929– Bank failures– Massive deflation– Stay on gold standard– 1 in 4 unemployed
![Page 8: Brain Teaser Two jars contain the same total numbers of balls, some blacks and some whites in each. From each urn are drawn n balls with replacement, where.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649de65503460f94ade869/html5/thumbnails/8.jpg)
During the crisis
• Great Recession– Housing crash– Lehman shock– Bank failures– Already stagnant
incomes collapse– Credit/liquidity
crisis
![Page 9: Brain Teaser Two jars contain the same total numbers of balls, some blacks and some whites in each. From each urn are drawn n balls with replacement, where.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649de65503460f94ade869/html5/thumbnails/9.jpg)
Reaction
• Great Depression– Bank holidays– New Deal (1st and 2nd)– Smoot-Hawley Tariff Act of
1930– Suspension of the gold
standard– Only recovered after World
War II
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Reaction
• Great Recession– TARP– ZLB and QE– Austerity and beyond– …
![Page 11: Brain Teaser Two jars contain the same total numbers of balls, some blacks and some whites in each. From each urn are drawn n balls with replacement, where.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649de65503460f94ade869/html5/thumbnails/11.jpg)
Comparisons
1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 7040
50
60
70
80
90
100
Slow and steady
Great Recession
Great Depression
Months after start of downturn
Indust
rial p
roduct
ion
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Comparisons
1929 1937 1945 1953 1961 1969 1977 1985 1993 2001 200960
70
80
90
100
110
120
130
Mercantile vs. open trade Terms of trade
1929 =
100
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Comparisons
1929 1937 1945 1953 1961 1969 1977 1985 1993 2001 200998.0%
98.5%
99.0%
99.5%
100.0%Foreign vs. domestic
GN
P a
s a %
of
GD
P
![Page 14: Brain Teaser Two jars contain the same total numbers of balls, some blacks and some whites in each. From each urn are drawn n balls with replacement, where.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649de65503460f94ade869/html5/thumbnails/14.jpg)
Comparisons
1920 1921 1922 1923 1924 1925 1926 1927 1928 1929 1930 1931 1932 1933 1934 1935 1936
-20%
-15%
-10%
-5%
0%
5%
10%
15%
20%
25%
30%
Sharp and cyclical world tradeSuez Canal Traffic
12-m
o M
A o
f yo
y ch
anges
(%)
![Page 15: Brain Teaser Two jars contain the same total numbers of balls, some blacks and some whites in each. From each urn are drawn n balls with replacement, where.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649de65503460f94ade869/html5/thumbnails/15.jpg)
Comparisons
1920 1924 1928 1932 1936 1940 19440%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
End of gold standard% of gold held by govt
% of gold held by public
![Page 16: Brain Teaser Two jars contain the same total numbers of balls, some blacks and some whites in each. From each urn are drawn n balls with replacement, where.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649de65503460f94ade869/html5/thumbnails/16.jpg)
Comparisons
1907 1911 1915 1919 1923 1927 1931 1935 1939 1943 1947 1951 19557
9
11
13
15
17
19
21
Paradox of thrift % of currency held by public
![Page 17: Brain Teaser Two jars contain the same total numbers of balls, some blacks and some whites in each. From each urn are drawn n balls with replacement, where.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649de65503460f94ade869/html5/thumbnails/17.jpg)
Comparisons
1910 1914 1918 1922 1926 1930 1934 193880
100
120
140
160
180
200
Deflation also sucks! Index of General Prices
1913 =
100
![Page 18: Brain Teaser Two jars contain the same total numbers of balls, some blacks and some whites in each. From each urn are drawn n balls with replacement, where.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649de65503460f94ade869/html5/thumbnails/18.jpg)
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