Proof of a Probability Problem by Induction
$begingroup$
Dear Statisticians and Mathematicians,
I am interested in proving the following lemma by induction
I have shown that it holds true for $n=2$ which I don't provide its proof here. We assume it is true when $n$ is replaced by $n-1$. I conditioned on $Y_1+...+Y_{n-1}$ but I could not prove. I don't know how to use the induction hypothesis to prove the lemma. I really appreciate any help of you guys in this regard.
probability probability-distributions conditional-probability order-statistics
edited Dec 13 '18 at 22:36
Math1000
19.3k31746
asked Dec 12 '18 at 0:46
DavidDavid
976
$endgroup$
add a comment |
$begingroup$
Dear Statisticians and Mathematicians,
I am interested in proving the following lemma by induction
I have shown that it holds true for $n=2$ which I don't provide its proof here. We assume it is true when $n$ is replaced by $n-1$. I conditioned on $Y_1+...+Y_{n-1}$ but I could not prove. I don't know how to use the induction hypothesis to prove the lemma. I really appreciate any help of you guys in this regard.
probability probability-distributions conditional-probability order-statistics
edited Dec 13 '18 at 22:36
Math1000
19.3k31746
asked Dec 12 '18 at 0:46
DavidDavid
976
$endgroup$
$begingroup$
Are you not satisfied with the proof that Ross provides in the text?
$endgroup$
– Math1000
Dec 13 '18 at 22:40
$begingroup$
@Math1000 Actually my adviser and I are looking for a simpler proof.
$endgroup$
– David
Jan 16 at 23:31
add a comment |
$begingroup$
Dear Statisticians and Mathematicians,
I am interested in proving the following lemma by induction
I have shown that it holds true for $n=2$ which I don't provide its proof here. We assume it is true when $n$ is replaced by $n-1$. I conditioned on $Y_1+...+Y_{n-1}$ but I could not prove. I don't know how to use the induction hypothesis to prove the lemma. I really appreciate any help of you guys in this regard.
probability probability-distributions conditional-probability order-statistics
edited Dec 13 '18 at 22:36
Math1000
19.3k31746
asked Dec 12 '18 at 0:46
DavidDavid
976
$endgroup$
Dear Statisticians and Mathematicians,
I am interested in proving the following lemma by induction
I have shown that it holds true for $n=2$ which I don't provide its proof here. We assume it is true when $n$ is replaced by $n-1$. I conditioned on $Y_1+...+Y_{n-1}$ but I could not prove. I don't know how to use the induction hypothesis to prove the lemma. I really appreciate any help of you guys in this regard.
probability probability-distributions conditional-probability order-statistics
probability probability-distributions conditional-probability order-statistics
edited Dec 13 '18 at 22:36
Math1000
19.3k31746
asked Dec 12 '18 at 0:46
DavidDavid
976
edited Dec 13 '18 at 22:36
Math1000
19.3k31746
asked Dec 12 '18 at 0:46
DavidDavid
976
edited Dec 13 '18 at 22:36
Math1000
19.3k31746
edited Dec 13 '18 at 22:36
Math1000
19.3k31746
edited Dec 13 '18 at 22:36
Math1000
19.3k31746
19.3k31746
asked Dec 12 '18 at 0:46
DavidDavid
976
asked Dec 12 '18 at 0:46
DavidDavid
976
asked Dec 12 '18 at 0:46
DavidDavid
976
976
$begingroup$
Are you not satisfied with the proof that Ross provides in the text?
$endgroup$
– Math1000
Dec 13 '18 at 22:40
$begingroup$
@Math1000 Actually my adviser and I are looking for a simpler proof.
$endgroup$
– David
Jan 16 at 23:31
add a comment |
$begingroup$
Are you not satisfied with the proof that Ross provides in the text?
$endgroup$
– Math1000
Dec 13 '18 at 22:40
$begingroup$
@Math1000 Actually my adviser and I are looking for a simpler proof.
$endgroup$
– David
Jan 16 at 23:31
$begingroup$
Are you not satisfied with the proof that Ross provides in the text?
$endgroup$
– Math1000
Dec 13 '18 at 22:40
$begingroup$
Are you not satisfied with the proof that Ross provides in the text?
$endgroup$
– Math1000
Dec 13 '18 at 22:40
$begingroup$
@Math1000 Actually my adviser and I are looking for a simpler proof.
$endgroup$
– David
Jan 16 at 23:31
$begingroup$
@Math1000 Actually my adviser and I are looking for a simpler proof.
$endgroup$
– David
Jan 16 at 23:31
add a comment |
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$begingroup$
Are you not satisfied with the proof that Ross provides in the text?
$endgroup$
– Math1000
Dec 13 '18 at 22:40
$begingroup$
@Math1000 Actually my adviser and I are looking for a simpler proof.
$endgroup$
– David
Jan 16 at 23:31