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kjetil b halvorsen ♦
kjetil b halvorsen ♦
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I was going through Chuong B Do' notes on The Multivariate Gaussian Distribution. The multivariate Gaussian distribution according to it, is given as follows:

$p(x; \mu, \Sigma) = \frac{1}{(2\pi)^{n/2}|\Sigma|^{1/2}} \exp(\frac{-1}{2}(x − \mu)^{T}\Sigma^{−1}(x − \mu))$$p(x; \mu, \Sigma) = \frac{1}{(2\pi)^{n/2}|\Sigma|^{1/2}} \exp(-\frac{1}{2}(x − \mu)^{T}\Sigma^{−1}(x − \mu))$

While attempting to come up to this conclusion myself I got stuck at,

$P(x_1,x_2) = P(x_1)P(x_2) = \frac{1}{2\pi\sigma^{2}}\exp(-\frac{1}{2\sigma^{2}}((x_1 - \mu_{X_1})^{2} + (x_2 - \mu_{X_2})^{2}))$

How can I relate the two equation or rather generalize the second one to reach to first?

I was going through Chuong B Do' notes on The Multivariate Gaussian Distribution. The multivariate Gaussian distribution according to it, is given as follows:

$p(x; \mu, \Sigma) = \frac{1}{(2\pi)^{n/2}|\Sigma|^{1/2}} \exp(\frac{-1}{2}(x − \mu)^{T}\Sigma^{−1}(x − \mu))$

While attempting to come up to this conclusion myself I got stuck at,

$P(x_1,x_2) = P(x_1)P(x_2) = \frac{1}{2\pi\sigma^{2}}\exp(-\frac{1}{2\sigma^{2}}((x_1 - \mu_{X_1})^{2} + (x_2 - \mu_{X_2})^{2}))$

How can I relate the two equation or rather generalize the second one to reach to first?

I was going through Chuong B Do' notes on The Multivariate Gaussian Distribution. The multivariate Gaussian distribution according to it, is given as follows:

$p(x; \mu, \Sigma) = \frac{1}{(2\pi)^{n/2}|\Sigma|^{1/2}} \exp(-\frac{1}{2}(x − \mu)^{T}\Sigma^{−1}(x − \mu))$

While attempting to come up to this conclusion myself I got stuck at,

$P(x_1,x_2) = P(x_1)P(x_2) = \frac{1}{2\pi\sigma^{2}}\exp(-\frac{1}{2\sigma^{2}}((x_1 - \mu_{X_1})^{2} + (x_2 - \mu_{X_2})^{2}))$

How can I relate the two equation or rather generalize the second one to reach to first?

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user256228
user256228

I was going through Chuong B Do' notes on The Multivariate Gaussian Distribution. The multivariate Gaussian distribution according to it, is given as follows:

$p(x; \mu, \Sigma) = \frac{1}{(2\pi)^{n/2}|\Sigma|^{1/2}} \exp(\frac{-1}{2}(x − \mu)^{T}\Sigma^{−1}(x − \mu))$

While attempting to come up to this conclusion myself I got stuck at,

$P(x_1,x_2) = P(x_1)P(x_2) = \frac{1}{\sqrt{2\pi\sigma^{2}}}\exp(-\frac{1}{2}((x_1 - \mu_{X_1})^{2} + (x_2 - \mu_{X_2})^{2}))$$P(x_1,x_2) = P(x_1)P(x_2) = \frac{1}{2\pi\sigma^{2}}\exp(-\frac{1}{2\sigma^{2}}((x_1 - \mu_{X_1})^{2} + (x_2 - \mu_{X_2})^{2}))$

How can I relate the two equation or rather generalize the second one to reach to first?

I was going through Chuong B Do' notes on The Multivariate Gaussian Distribution. The multivariate Gaussian distribution according to it, is given as follows:

$p(x; \mu, \Sigma) = \frac{1}{(2\pi)^{n/2}|\Sigma|^{1/2}} \exp(\frac{-1}{2}(x − \mu)^{T}\Sigma^{−1}(x − \mu))$

While attempting to come up to this conclusion myself I got stuck at,

$P(x_1,x_2) = P(x_1)P(x_2) = \frac{1}{\sqrt{2\pi\sigma^{2}}}\exp(-\frac{1}{2}((x_1 - \mu_{X_1})^{2} + (x_2 - \mu_{X_2})^{2}))$

How can I relate the two equation or rather generalize the second one to reach to first?

I was going through Chuong B Do' notes on The Multivariate Gaussian Distribution. The multivariate Gaussian distribution according to it, is given as follows:

$p(x; \mu, \Sigma) = \frac{1}{(2\pi)^{n/2}|\Sigma|^{1/2}} \exp(\frac{-1}{2}(x − \mu)^{T}\Sigma^{−1}(x − \mu))$

While attempting to come up to this conclusion myself I got stuck at,

$P(x_1,x_2) = P(x_1)P(x_2) = \frac{1}{2\pi\sigma^{2}}\exp(-\frac{1}{2\sigma^{2}}((x_1 - \mu_{X_1})^{2} + (x_2 - \mu_{X_2})^{2}))$

How can I relate the two equation or rather generalize the second one to reach to first?

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Siong Thye Goh
Siong Thye Goh
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I was going through Chuong B Do' notes on The Multivariate Gaussian Distribution. The multivariate Gaussian distribution according to it, is given as follows:

$p(x; µ, Σ) = \frac{1}{(2π)^{n/2}|Σ|^{1/2}} exp(\frac{-1}{2}(x − µ)^{T}Σ^{−1}(x − µ))$$p(x; \mu, \Sigma) = \frac{1}{(2\pi)^{n/2}|\Sigma|^{1/2}} \exp(\frac{-1}{2}(x − \mu)^{T}\Sigma^{−1}(x − \mu))$

While attempting to come up to this conclusion myself I got stuck at,

$P(x1,x2) = P(x1)P(x2) = \frac{1}{\sqrt{2π\sigma^{2}}}exp(-\frac{1}{2}((x1 - \mu_{x1})^{2} + (x2 - \mu_{x2})^{2}))$$P(x_1,x_2) = P(x_1)P(x_2) = \frac{1}{\sqrt{2\pi\sigma^{2}}}\exp(-\frac{1}{2}((x_1 - \mu_{X_1})^{2} + (x_2 - \mu_{X_2})^{2}))$

How can I relate the two equation or rather generalize the second one to reach to first?

I was going through Chuong B Do' notes on The Multivariate Gaussian Distribution. The multivariate Gaussian distribution according to it, is given as follows:

$p(x; µ, Σ) = \frac{1}{(2π)^{n/2}|Σ|^{1/2}} exp(\frac{-1}{2}(x − µ)^{T}Σ^{−1}(x − µ))$

While attempting to come up to this conclusion myself I got stuck at,

$P(x1,x2) = P(x1)P(x2) = \frac{1}{\sqrt{2π\sigma^{2}}}exp(-\frac{1}{2}((x1 - \mu_{x1})^{2} + (x2 - \mu_{x2})^{2}))$

How can I relate the two equation or rather generalize the second one to reach to first?

I was going through Chuong B Do' notes on The Multivariate Gaussian Distribution. The multivariate Gaussian distribution according to it, is given as follows:

$p(x; \mu, \Sigma) = \frac{1}{(2\pi)^{n/2}|\Sigma|^{1/2}} \exp(\frac{-1}{2}(x − \mu)^{T}\Sigma^{−1}(x − \mu))$

While attempting to come up to this conclusion myself I got stuck at,

$P(x_1,x_2) = P(x_1)P(x_2) = \frac{1}{\sqrt{2\pi\sigma^{2}}}\exp(-\frac{1}{2}((x_1 - \mu_{X_1})^{2} + (x_2 - \mu_{X_2})^{2}))$

How can I relate the two equation or rather generalize the second one to reach to first?

added 38 characters in body
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user256228
user256228
Source Link
user256228
user256228