Approximation - how to graph a probability density function?
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I was wondering how to graph a probability density function with the following information: https://prnt.sc/lpvnxm.
calculus
asked Dec 3 '18 at 2:13
Andy ZhangAndy Zhang
6
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add a comment |
$begingroup$
I was wondering how to graph a probability density function with the following information: https://prnt.sc/lpvnxm.
calculus
asked Dec 3 '18 at 2:13
Andy ZhangAndy Zhang
6
$endgroup$
$begingroup$
It's better to write the full question here rather than linking to an image. Also, you'll get a better response if you explain what you've tried.
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– littleO
Dec 3 '18 at 2:43
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Related: math.stackexchange.com/q/97/3301 and information on pdf or erf
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– ja72
Dec 3 '18 at 3:56
add a comment |
$begingroup$
I was wondering how to graph a probability density function with the following information: https://prnt.sc/lpvnxm.
calculus
asked Dec 3 '18 at 2:13
Andy ZhangAndy Zhang
6
$endgroup$
I was wondering how to graph a probability density function with the following information: https://prnt.sc/lpvnxm.
calculus
calculus
asked Dec 3 '18 at 2:13
Andy ZhangAndy Zhang
6
asked Dec 3 '18 at 2:13
Andy ZhangAndy Zhang
6
asked Dec 3 '18 at 2:13
Andy ZhangAndy Zhang
6
asked Dec 3 '18 at 2:13
Andy ZhangAndy Zhang
6
asked Dec 3 '18 at 2:13
Andy ZhangAndy Zhang
6
6
$begingroup$
It's better to write the full question here rather than linking to an image. Also, you'll get a better response if you explain what you've tried.
$endgroup$
– littleO
Dec 3 '18 at 2:43
$begingroup$
Related: math.stackexchange.com/q/97/3301 and information on pdf or erf
$endgroup$
– ja72
Dec 3 '18 at 3:56
add a comment |
$begingroup$
It's better to write the full question here rather than linking to an image. Also, you'll get a better response if you explain what you've tried.
$endgroup$
– littleO
Dec 3 '18 at 2:43
$begingroup$
Related: math.stackexchange.com/q/97/3301 and information on pdf or erf
$endgroup$
– ja72
Dec 3 '18 at 3:56
$begingroup$
It's better to write the full question here rather than linking to an image. Also, you'll get a better response if you explain what you've tried.
$endgroup$
– littleO
Dec 3 '18 at 2:43
$begingroup$
It's better to write the full question here rather than linking to an image. Also, you'll get a better response if you explain what you've tried.
$endgroup$
– littleO
Dec 3 '18 at 2:43
$begingroup$
Related: math.stackexchange.com/q/97/3301 and information on pdf or erf
$endgroup$
– ja72
Dec 3 '18 at 3:56
$begingroup$
Related: math.stackexchange.com/q/97/3301 and information on pdf or erf
$endgroup$
– ja72
Dec 3 '18 at 3:56
add a comment |
1 Answer
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oldest
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$$ f(x) = frac{1}{ sqrt{ 2 pi sigma }} exp bigg( - frac{ (x - mu )^2 }{2 sigma^2 } bigg)$$
Since $e^x approx 1+x $
the Quadratic approximation must be
$$ Q(x) = K bigg(1 - frac{ (x - mu )^2 }{2 sigma^2} bigg)$$
Only valid for $|x - mu | < sqrt2 sigma $
$K$ is a normalization constant that you can calculate by making the requirement
$$ int _{mu- sqrt2 sigma} ^{mu-+sqrt2 sigma} Q(x)dx = 1$$
answered Dec 3 '18 at 2:45
WW1WW1
7,3151712
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
$$ f(x) = frac{1}{ sqrt{ 2 pi sigma }} exp bigg( - frac{ (x - mu )^2 }{2 sigma^2 } bigg)$$
Since $e^x approx 1+x $
the Quadratic approximation must be
$$ Q(x) = K bigg(1 - frac{ (x - mu )^2 }{2 sigma^2} bigg)$$
Only valid for $|x - mu | < sqrt2 sigma $
$K$ is a normalization constant that you can calculate by making the requirement
$$ int _{mu- sqrt2 sigma} ^{mu-+sqrt2 sigma} Q(x)dx = 1$$
answered Dec 3 '18 at 2:45
WW1WW1
7,3151712
$endgroup$
add a comment |
$begingroup$
$$ f(x) = frac{1}{ sqrt{ 2 pi sigma }} exp bigg( - frac{ (x - mu )^2 }{2 sigma^2 } bigg)$$
Since $e^x approx 1+x $
the Quadratic approximation must be
$$ Q(x) = K bigg(1 - frac{ (x - mu )^2 }{2 sigma^2} bigg)$$
Only valid for $|x - mu | < sqrt2 sigma $
$K$ is a normalization constant that you can calculate by making the requirement
$$ int _{mu- sqrt2 sigma} ^{mu-+sqrt2 sigma} Q(x)dx = 1$$
answered Dec 3 '18 at 2:45
WW1WW1
7,3151712
$endgroup$
add a comment |
$begingroup$
$$ f(x) = frac{1}{ sqrt{ 2 pi sigma }} exp bigg( - frac{ (x - mu )^2 }{2 sigma^2 } bigg)$$
Since $e^x approx 1+x $
the Quadratic approximation must be
$$ Q(x) = K bigg(1 - frac{ (x - mu )^2 }{2 sigma^2} bigg)$$
Only valid for $|x - mu | < sqrt2 sigma $
$K$ is a normalization constant that you can calculate by making the requirement
$$ int _{mu- sqrt2 sigma} ^{mu-+sqrt2 sigma} Q(x)dx = 1$$
answered Dec 3 '18 at 2:45
WW1WW1
7,3151712
$endgroup$
$$ f(x) = frac{1}{ sqrt{ 2 pi sigma }} exp bigg( - frac{ (x - mu )^2 }{2 sigma^2 } bigg)$$
Since $e^x approx 1+x $
the Quadratic approximation must be
$$ Q(x) = K bigg(1 - frac{ (x - mu )^2 }{2 sigma^2} bigg)$$
Only valid for $|x - mu | < sqrt2 sigma $
$K$ is a normalization constant that you can calculate by making the requirement
$$ int _{mu- sqrt2 sigma} ^{mu-+sqrt2 sigma} Q(x)dx = 1$$
answered Dec 3 '18 at 2:45
WW1WW1
7,3151712
answered Dec 3 '18 at 2:45
WW1WW1
7,3151712
answered Dec 3 '18 at 2:45
WW1WW1
7,3151712
answered Dec 3 '18 at 2:45
WW1WW1
7,3151712
7,3151712
add a comment |
add a comment |
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$begingroup$
It's better to write the full question here rather than linking to an image. Also, you'll get a better response if you explain what you've tried.
$endgroup$
– littleO
Dec 3 '18 at 2:43
$begingroup$
Related: math.stackexchange.com/q/97/3301 and information on pdf or erf
$endgroup$
– ja72
Dec 3 '18 at 3:56