The correct answer is $\frac{{{\text{p}}\left( {{\text{p}} + 1} \right)}}{2}$.
A Gaussian distribution is a probability distribution that is often used to model real-world data. It is also known as a normal distribution. The Gaussian distribution is characterized by its mean and variance. The mean is the average of the data, and the variance is a measure of how spread out the data is.
In a P dimensional Gaussian distribution model, there are P parameters that need to be estimated: the mean and variance for each of the P dimensions. Therefore, the total number of independent parameters that need to be estimated is $\frac{{{\text{p}}\left( {{\text{p}} + 1} \right)}}{2}$.
Option A is incorrect because it only considers the mean. Option B is incorrect because it only considers the variance. Option C is incorrect because it is not a whole number. Option D is incorrect because it is too large.