By default, C++ makes all class variables and functions private. That means you can actually declare private variables and functions at the top of your class declaration without even labeling them private:
Instead of writing the entire declaration twice, a better option is to put the declaration into a header file. Then you can include the entire declaration with a single line of code:
class Gaussian
{
public:
float mu, sigma2;
// constructor functions
Gaussian ();
Gaussian (float, float);
// functions to evaluate
float evaluate (float);
Gaussian mul (Gaussian);
Gaussian add (Gaussian);
};