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I am trying to solve a problem about my homework. The problem says that

Assume a two-class problem with equal a priori class probabilities

Does it mean, mean vectors and covariance matrices should be equal?

The question of the homework is:

Assume a two-class problem with equal a priori class probabilities and Gaussian class-conditional densities as follows:

$$p(x\mid w_1) = {\cal N}\left(\begin{bmatrix} 0 \\ 0 \end{bmatrix},\begin{bmatrix} a & c \\ c & b \end{bmatrix}\right)\quad\text{and}\quad p(x\mid w_2) = {\cal N}\left(\begin{bmatrix} d \\ e \end{bmatrix},\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}\right)$$

where $ab-c^2=1$.

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    $\begingroup$ Basically, it means that $\text{Prob}(w_1)=0.5$ and $\text{Prob}(w_2)=0.5$ $\endgroup$ – varty Nov 12 '11 at 19:47
  • $\begingroup$ @varty, thank you. I thought it was more complex :) $\endgroup$ – user7345 Nov 12 '11 at 20:03
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It means that in the population, the prior probability that a sample belongs to either of the two classes is equal. Think of a fair coin; at each toss of the coin there is a 0.5 probability that the toss will result in a head or a tail.

If the class prior probabilities were not equal, that would indicate that in the population one of the two classes was more prevalent than the other.

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