Explanation
The total number of clicks is the sum of the number of men and
women. The sum of two Poisson random variables also follows a Poisson distribution with rate equal to the sum of their rates.
The Normal and Binomial distribution can approximate the Poisson distribution in certain cases, but the expressions above do not approximate Poisson(X+Y).

Explanation
A linear scaling of the input variables (that may be caused by a change of units for the measurements) is sufficient to modify the PCA results. Feature selection methods that are sufficient for simple distributions of the patterns belonging to different classes can fail in classification tasks with complex decision boundaries. In addition, methods based on a linear dependence (like the correlation) cannot take care of arbitrary relations between the pattern coordinates and the different classes. On the contrary, the mutual information can measure arbitrary relations between variables and it does not depend on transformations acting on the different variables.
This item concerns itself with feature selection for a text classification problem and references mutual information criteria. Mutual information is a bit more sophisticated than just selecting based on the simple correlation of two numbers because it can detect non-linear relationships that will not be identified by the correlation. Whenever possible: mutual information is a better feature selection technique than correlation.
Mutual information is a quantification of the dependency between random variables. It is sometimes contrasted with linear correlation since mutual information captures nonlinear dependence.
Correlation analysis provides a quantitative means of measuring the strength of a linear relationship between two vectors of data. Mutual information is essentially the measure of how much "knowledge" one can gain of a certain variable by knowing the value of another variable.

Explanation
From the definition, P(A,B|C) P(B|C) =P(A,B.C)/P(C) P(B.C)/P(C) =P(A,B.C) P(B,C) =P(A|BC) This follows from the definition of conditional probability, applied twice: P(A,B)=(PA|B)P(B)