Mixing
What distribution does $X/Y$ have if $X$ and $Y$ are normal distributed independent variables?
0
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Let $X,Ysim N(0,1)$ iid. What distribution would the variable $frac{X}{Y}$ follow? Intuitively it would have an expected value of $1$. Or would it?
probability normal-distribution
asked Jan 30 at 14:30
John CataldoJohn Cataldo
1,1931316
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add a comment |
0
$begingroup$
Let $X,Ysim N(0,1)$ iid. What distribution would the variable $frac{X}{Y}$ follow? Intuitively it would have an expected value of $1$. Or would it?
probability normal-distribution
asked Jan 30 at 14:30
John CataldoJohn Cataldo
1,1931316
$endgroup$
2
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It's a Cauchy distribution, which has no well-defined mean: en.wikipedia.org/wiki/Cauchy_distribution
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– Adrian Keister
Jan 30 at 14:35
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See math.stackexchange.com/questions/77873/….
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– StubbornAtom
Jan 30 at 14:52
add a comment |
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0
1
$begingroup$
Let $X,Ysim N(0,1)$ iid. What distribution would the variable $frac{X}{Y}$ follow? Intuitively it would have an expected value of $1$. Or would it?
probability normal-distribution
asked Jan 30 at 14:30
John CataldoJohn Cataldo
1,1931316
$endgroup$
Let $X,Ysim N(0,1)$ iid. What distribution would the variable $frac{X}{Y}$ follow? Intuitively it would have an expected value of $1$. Or would it?
probability normal-distribution
probability normal-distribution
asked Jan 30 at 14:30
John CataldoJohn Cataldo
1,1931316
asked Jan 30 at 14:30
John CataldoJohn Cataldo
1,1931316
asked Jan 30 at 14:30
John CataldoJohn Cataldo
1,1931316
asked Jan 30 at 14:30
John CataldoJohn Cataldo
1,1931316
asked Jan 30 at 14:30
John CataldoJohn Cataldo
1,1931316
1,1931316
2
$begingroup$
It's a Cauchy distribution, which has no well-defined mean: en.wikipedia.org/wiki/Cauchy_distribution
$endgroup$
– Adrian Keister
Jan 30 at 14:35
$begingroup$
See math.stackexchange.com/questions/77873/….
$endgroup$
– StubbornAtom
Jan 30 at 14:52
add a comment |
2
$begingroup$
It's a Cauchy distribution, which has no well-defined mean: en.wikipedia.org/wiki/Cauchy_distribution
$endgroup$
– Adrian Keister
Jan 30 at 14:35
$begingroup$
See math.stackexchange.com/questions/77873/….
$endgroup$
– StubbornAtom
Jan 30 at 14:52
2
2
$begingroup$
It's a Cauchy distribution, which has no well-defined mean: en.wikipedia.org/wiki/Cauchy_distribution
$endgroup$
– Adrian Keister
Jan 30 at 14:35
$begingroup$
It's a Cauchy distribution, which has no well-defined mean: en.wikipedia.org/wiki/Cauchy_distribution
$endgroup$
– Adrian Keister
Jan 30 at 14:35
$begingroup$
See math.stackexchange.com/questions/77873/….
$endgroup$
– StubbornAtom
Jan 30 at 14:52
$begingroup$
See math.stackexchange.com/questions/77873/….
$endgroup$
– StubbornAtom
Jan 30 at 14:52
add a comment |
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2
$begingroup$
It's a Cauchy distribution, which has no well-defined mean: en.wikipedia.org/wiki/Cauchy_distribution
$endgroup$
– Adrian Keister
Jan 30 at 14:35
$begingroup$
See math.stackexchange.com/questions/77873/….
$endgroup$
– StubbornAtom
Jan 30 at 14:52