is the formula of cdf of standard normal distribution in nist wrong?Prove normalizing constant on normal CDFHard integral that standard CAS get totally wrongSecond moment of the product of normal cdf & pdfsolving/approximating integral of standard normal cdfHow to integrate standard normal cdf to nth powerIntegral involving CDF of a standard normal random variableExpected Value of Normal Random Variable times its CDFIntegral of product of CDF and PDF 0f standard normal distributionIndefinite integral involving normal cdfError in proof of MGF of standard half normal distribution?
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is the formula of cdf of standard normal distribution in nist wrong?
Prove normalizing constant on normal CDFHard integral that standard CAS get totally wrongSecond moment of the product of normal cdf & pdfsolving/approximating integral of standard normal cdfHow to integrate standard normal cdf to nth powerIntegral involving CDF of a standard normal random variableExpected Value of Normal Random Variable times its CDFIntegral of product of CDF and PDF 0f standard normal distributionIndefinite integral involving normal cdfError in proof of MGF of standard half normal distribution?
$begingroup$
this formula comes from nist
$$
F(x) = int_-infty^x frace^-x^2/2 sqrt2pi
$$
which is different from this wiki version
$$
F(x) = int_-infty^x frace^-t^2/2 sqrt2pi dt
$$
is the nist version wrong? or it is appropriate way to write a integral formula omitting dt?
integration
asked Mar 22 at 2:53
shiqangpanshiqangpan
152
$endgroup$
add a comment |
$begingroup$
this formula comes from nist
$$
F(x) = int_-infty^x frace^-x^2/2 sqrt2pi
$$
which is different from this wiki version
$$
F(x) = int_-infty^x frace^-t^2/2 sqrt2pi dt
$$
is the nist version wrong? or it is appropriate way to write a integral formula omitting dt?
integration
asked Mar 22 at 2:53
shiqangpanshiqangpan
152
$endgroup$
add a comment |
$begingroup$
this formula comes from nist
$$
F(x) = int_-infty^x frace^-x^2/2 sqrt2pi
$$
which is different from this wiki version
$$
F(x) = int_-infty^x frace^-t^2/2 sqrt2pi dt
$$
is the nist version wrong? or it is appropriate way to write a integral formula omitting dt?
integration
asked Mar 22 at 2:53
shiqangpanshiqangpan
152
$endgroup$
this formula comes from nist
$$
F(x) = int_-infty^x frace^-x^2/2 sqrt2pi
$$
which is different from this wiki version
$$
F(x) = int_-infty^x frace^-t^2/2 sqrt2pi dt
$$
is the nist version wrong? or it is appropriate way to write a integral formula omitting dt?
integration
integration
asked Mar 22 at 2:53
shiqangpanshiqangpan
152
asked Mar 22 at 2:53
shiqangpanshiqangpan
152
asked Mar 22 at 2:53
shiqangpanshiqangpan
152
asked Mar 22 at 2:53
shiqangpanshiqangpan
152
asked Mar 22 at 2:53
shiqangpanshiqangpan
152
152
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
There should be a $dt$. Also, the variable of integration should be something other than $x$ (since $x$ is used as the argument of $F$). But it can be pretty much anything else, like $a,y,u$, etc. So you could also write $$F(x) = int_-infty^x dfrace^-y^2/2sqrt2pi, dy,$$ for example. (The variable of integration is a "dummy variable".)
answered Mar 22 at 2:57
Minus One-TwelfthMinus One-Twelfth
3,233413
$endgroup$
add a comment |
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1 Answer
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$begingroup$
There should be a $dt$. Also, the variable of integration should be something other than $x$ (since $x$ is used as the argument of $F$). But it can be pretty much anything else, like $a,y,u$, etc. So you could also write $$F(x) = int_-infty^x dfrace^-y^2/2sqrt2pi, dy,$$ for example. (The variable of integration is a "dummy variable".)
answered Mar 22 at 2:57
Minus One-TwelfthMinus One-Twelfth
3,233413
$endgroup$
add a comment |
$begingroup$
There should be a $dt$. Also, the variable of integration should be something other than $x$ (since $x$ is used as the argument of $F$). But it can be pretty much anything else, like $a,y,u$, etc. So you could also write $$F(x) = int_-infty^x dfrace^-y^2/2sqrt2pi, dy,$$ for example. (The variable of integration is a "dummy variable".)
answered Mar 22 at 2:57
Minus One-TwelfthMinus One-Twelfth
3,233413
$endgroup$
add a comment |
$begingroup$
There should be a $dt$. Also, the variable of integration should be something other than $x$ (since $x$ is used as the argument of $F$). But it can be pretty much anything else, like $a,y,u$, etc. So you could also write $$F(x) = int_-infty^x dfrace^-y^2/2sqrt2pi, dy,$$ for example. (The variable of integration is a "dummy variable".)
answered Mar 22 at 2:57
Minus One-TwelfthMinus One-Twelfth
3,233413
$endgroup$
There should be a $dt$. Also, the variable of integration should be something other than $x$ (since $x$ is used as the argument of $F$). But it can be pretty much anything else, like $a,y,u$, etc. So you could also write $$F(x) = int_-infty^x dfrace^-y^2/2sqrt2pi, dy,$$ for example. (The variable of integration is a "dummy variable".)
answered Mar 22 at 2:57
Minus One-TwelfthMinus One-Twelfth
3,233413
answered Mar 22 at 2:57
Minus One-TwelfthMinus One-Twelfth
3,233413
answered Mar 22 at 2:57
Minus One-TwelfthMinus One-Twelfth
3,233413
answered Mar 22 at 2:57
Minus One-TwelfthMinus One-Twelfth
3,233413
3,233413
add a comment |
add a comment |
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