Closed form solutions to a Gaussian equation
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Let $phi(t) := frac{1}{sqrt{2pi}}exp{-t^2/2}$ be the standard Gaussian pdf function and $Phi(t) := int_{-infty}^t phi(u)du$ be the Gaussian CDF function. Consider equation
$$
Phi(x) + phi(x) = 1.
$$
I'm wondering whether such an equation has simple closed-form solutions $x$?
probability gaussian-integral transcendental-equations
edited Nov 15 at 19:25
Alejandro Nasif Salum
3,629117
asked Nov 15 at 19:08
Yining Wang
774315
add a comment |
up vote
0
down vote
favorite
Let $phi(t) := frac{1}{sqrt{2pi}}exp{-t^2/2}$ be the standard Gaussian pdf function and $Phi(t) := int_{-infty}^t phi(u)du$ be the Gaussian CDF function. Consider equation
$$
Phi(x) + phi(x) = 1.
$$
I'm wondering whether such an equation has simple closed-form solutions $x$?
probability gaussian-integral transcendental-equations
edited Nov 15 at 19:25
Alejandro Nasif Salum
3,629117
asked Nov 15 at 19:08
Yining Wang
774315
If you still interested in an answer give a reply.
– callculus
Nov 16 at 12:40
Looks like $x=39.9$ (wolframalpha.com/input/…).
– StubbornAtom
Nov 16 at 15:14
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Let $phi(t) := frac{1}{sqrt{2pi}}exp{-t^2/2}$ be the standard Gaussian pdf function and $Phi(t) := int_{-infty}^t phi(u)du$ be the Gaussian CDF function. Consider equation
$$
Phi(x) + phi(x) = 1.
$$
I'm wondering whether such an equation has simple closed-form solutions $x$?
probability gaussian-integral transcendental-equations
edited Nov 15 at 19:25
Alejandro Nasif Salum
3,629117
asked Nov 15 at 19:08
Yining Wang
774315
Let $phi(t) := frac{1}{sqrt{2pi}}exp{-t^2/2}$ be the standard Gaussian pdf function and $Phi(t) := int_{-infty}^t phi(u)du$ be the Gaussian CDF function. Consider equation
$$
Phi(x) + phi(x) = 1.
$$
I'm wondering whether such an equation has simple closed-form solutions $x$?
probability gaussian-integral transcendental-equations
probability gaussian-integral transcendental-equations
edited Nov 15 at 19:25
Alejandro Nasif Salum
3,629117
asked Nov 15 at 19:08
Yining Wang
774315
edited Nov 15 at 19:25
Alejandro Nasif Salum
3,629117
asked Nov 15 at 19:08
Yining Wang
774315
edited Nov 15 at 19:25
Alejandro Nasif Salum
3,629117
edited Nov 15 at 19:25
Alejandro Nasif Salum
3,629117
edited Nov 15 at 19:25
Alejandro Nasif Salum
3,629117
3,629117
asked Nov 15 at 19:08
Yining Wang
774315
asked Nov 15 at 19:08
Yining Wang
774315
asked Nov 15 at 19:08
Yining Wang
774315
774315
If you still interested in an answer give a reply.
– callculus
Nov 16 at 12:40
Looks like $x=39.9$ (wolframalpha.com/input/…).
– StubbornAtom
Nov 16 at 15:14
add a comment |
If you still interested in an answer give a reply.
– callculus
Nov 16 at 12:40
Looks like $x=39.9$ (wolframalpha.com/input/…).
– StubbornAtom
Nov 16 at 15:14
If you still interested in an answer give a reply.
– callculus
Nov 16 at 12:40
If you still interested in an answer give a reply.
– callculus
Nov 16 at 12:40
Looks like $x=39.9$ (wolframalpha.com/input/…).
– StubbornAtom
Nov 16 at 15:14
Looks like $x=39.9$ (wolframalpha.com/input/…).
– StubbornAtom
Nov 16 at 15:14
add a comment |
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If you still interested in an answer give a reply.
– callculus
Nov 16 at 12:40
Looks like $x=39.9$ (wolframalpha.com/input/…).
– StubbornAtom
Nov 16 at 15:14