Question

Modify the model Maximum likelihood to estimate $\mu^1$, $\mu^2$ and $\Sigma$ "Water" type Pokémons: $x_1, x_2, x_3, \dots, x_{79}$ "Normal" type Pokémons: $x_{80}, x_{81}, x_{82}, \dots, x_{140}$ $\mu^1$ $\Sigma$ $\mu^2$ Classification based on: $P(C_1|x) = \frac{P(x|C_1)P(C_1)}{P(x|C_1)P(C_1) + P(x|C_2)P(C_2)}$ Assign the observation which maximize $P(C_1|x)$ or equivalently $\delta_k(x) = x^T \Sigma^{-1} \mu_k - \frac{1}{2} \mu_k^T \Sigma^{-1} \mu_k + log \ p_k$ Where $p_k = P(C_k)$

          Modify the model
Maximum likelihood to estimate $\mu^1$, $\mu^2$ and $\Sigma$
"Water" type Pokémons:
$x_1, x_2, x_3, \dots, x_{79}$
"Normal" type Pokémons:
$x_{80}, x_{81}, x_{82}, \dots, x_{140}$
$\mu^1$   $\Sigma$   $\mu^2$
Classification based on: $P(C_1|x) = \frac{P(x|C_1)P(C_1)}{P(x|C_1)P(C_1) + P(x|C_2)P(C_2)}$
Assign the observation which maximize $P(C_1|x)$ or equivalently
$\delta_k(x) = x^T \Sigma^{-1} \mu_k - \frac{1}{2} \mu_k^T \Sigma^{-1} \mu_k + log \ p_k$
Where $p_k = P(C_k)$

Modify the model
Maximum likelihood to estimate μ^1, μ^2 and Σ
"Water" type Pokémons:
x1, x2, x3, …, x79
"Normal" type Pokémons:
x80, x81, x82, …, x140
μ^1 Σ μ^2
Classification based on: P(C1|x) = (P(x|C1)P(C1))/(P(x|C1)P(C1) + P(x|C2)P(C2))
Assign the observation which maximize P(C1|x) or equivalently
(x) = x^T Σ^-1 - (1)/(2)^T Σ^-1 + log pk
Where pk = P(Ck)

Added by Diana A.

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