Derivation of univariate normal distribution and how it approximates binomial distribution problems

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Can some one kindly explain the derivation of normal distribution (univariate) and how it could be approximated for binomial distribution (coin flip problem)? I have searched for hours but could not find any online.



I would like to know how to arrive at below formula and how it helps solve binomial distribution problem:

$f(x) = dfrac 1sigma surd2 pitextexpBig( dfrac 12(dfrac x-musigmaBig)Big)$



I am at a simple binomial distribution problem:

$displaystyle P(X=k)=n choose kp^k(1-p)^n-k$




normal-distribution binomial-distribution central-limit-theorem




share|cite|improve this question





















  • What do you mean by a "proof" of a distribution?
    – Randall
    Jul 26 at 15:02










  • Derivation of f(x) noted above and how it first for binomial distribution. I have updated now accordingly. Its clearer now?
    – Paari Vendhan
    Jul 26 at 15:05











  • Yes. You wish to know why the normal is a reasonable approximation to a binomial (under certain conditions).
    – Randall
    Jul 26 at 15:07










  • and also how to arrive at that formula f(x) if possible in context of binomial distribution problem itself
    – Paari Vendhan
    Jul 26 at 15:08










  • De Moivre-Laplace theorem
    – Robert Israel
    Jul 26 at 15:12














up vote
0
down vote

favorite












Can some one kindly explain the derivation of normal distribution (univariate) and how it could be approximated for binomial distribution (coin flip problem)? I have searched for hours but could not find any online.



I would like to know how to arrive at below formula and how it helps solve binomial distribution problem:

$f(x) = dfrac 1sigma surd2 pitextexpBig( dfrac 12(dfrac x-musigmaBig)Big)$



I am at a simple binomial distribution problem:

$displaystyle P(X=k)=n choose kp^k(1-p)^n-k$




normal-distribution binomial-distribution central-limit-theorem




share|cite|improve this question





















  • What do you mean by a "proof" of a distribution?
    – Randall
    Jul 26 at 15:02










  • Derivation of f(x) noted above and how it first for binomial distribution. I have updated now accordingly. Its clearer now?
    – Paari Vendhan
    Jul 26 at 15:05











  • Yes. You wish to know why the normal is a reasonable approximation to a binomial (under certain conditions).
    – Randall
    Jul 26 at 15:07










  • and also how to arrive at that formula f(x) if possible in context of binomial distribution problem itself
    – Paari Vendhan
    Jul 26 at 15:08










  • De Moivre-Laplace theorem
    – Robert Israel
    Jul 26 at 15:12












up vote
0
down vote

favorite









up vote
0
down vote

favorite











Can some one kindly explain the derivation of normal distribution (univariate) and how it could be approximated for binomial distribution (coin flip problem)? I have searched for hours but could not find any online.



I would like to know how to arrive at below formula and how it helps solve binomial distribution problem:

$f(x) = dfrac 1sigma surd2 pitextexpBig( dfrac 12(dfrac x-musigmaBig)Big)$



I am at a simple binomial distribution problem:

$displaystyle P(X=k)=n choose kp^k(1-p)^n-k$




normal-distribution binomial-distribution central-limit-theorem




share|cite|improve this question













Can some one kindly explain the derivation of normal distribution (univariate) and how it could be approximated for binomial distribution (coin flip problem)? I have searched for hours but could not find any online.



I would like to know how to arrive at below formula and how it helps solve binomial distribution problem:

$f(x) = dfrac 1sigma surd2 pitextexpBig( dfrac 12(dfrac x-musigmaBig)Big)$



I am at a simple binomial distribution problem:

$displaystyle P(X=k)=n choose kp^k(1-p)^n-k$





normal-distribution binomial-distribution central-limit-theorem





share|cite|improve this question












share|cite|improve this question




share|cite|improve this question








edited Jul 26 at 15:07
























asked Jul 26 at 15:01









Paari Vendhan

455




455











  • What do you mean by a "proof" of a distribution?
    – Randall
    Jul 26 at 15:02










  • Derivation of f(x) noted above and how it first for binomial distribution. I have updated now accordingly. Its clearer now?
    – Paari Vendhan
    Jul 26 at 15:05











  • Yes. You wish to know why the normal is a reasonable approximation to a binomial (under certain conditions).
    – Randall
    Jul 26 at 15:07










  • and also how to arrive at that formula f(x) if possible in context of binomial distribution problem itself
    – Paari Vendhan
    Jul 26 at 15:08










  • De Moivre-Laplace theorem
    – Robert Israel
    Jul 26 at 15:12
















  • What do you mean by a "proof" of a distribution?
    – Randall
    Jul 26 at 15:02










  • Derivation of f(x) noted above and how it first for binomial distribution. I have updated now accordingly. Its clearer now?
    – Paari Vendhan
    Jul 26 at 15:05











  • Yes. You wish to know why the normal is a reasonable approximation to a binomial (under certain conditions).
    – Randall
    Jul 26 at 15:07










  • and also how to arrive at that formula f(x) if possible in context of binomial distribution problem itself
    – Paari Vendhan
    Jul 26 at 15:08










  • De Moivre-Laplace theorem
    – Robert Israel
    Jul 26 at 15:12















What do you mean by a "proof" of a distribution?
– Randall
Jul 26 at 15:02




What do you mean by a "proof" of a distribution?
– Randall
Jul 26 at 15:02












Derivation of f(x) noted above and how it first for binomial distribution. I have updated now accordingly. Its clearer now?
– Paari Vendhan
Jul 26 at 15:05





Derivation of f(x) noted above and how it first for binomial distribution. I have updated now accordingly. Its clearer now?
– Paari Vendhan
Jul 26 at 15:05













Yes. You wish to know why the normal is a reasonable approximation to a binomial (under certain conditions).
– Randall
Jul 26 at 15:07




Yes. You wish to know why the normal is a reasonable approximation to a binomial (under certain conditions).
– Randall
Jul 26 at 15:07












and also how to arrive at that formula f(x) if possible in context of binomial distribution problem itself
– Paari Vendhan
Jul 26 at 15:08




and also how to arrive at that formula f(x) if possible in context of binomial distribution problem itself
– Paari Vendhan
Jul 26 at 15:08












De Moivre-Laplace theorem
– Robert Israel
Jul 26 at 15:12




De Moivre-Laplace theorem
– Robert Israel
Jul 26 at 15:12















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