Question

A univariate Gaussian Mixture Model (GMM) with two components, each having its own mean and standard deviation, how many parameters are needed to fully define the model?

A. 2

B. 3

C. 4

D. 5

Answer 1

To fully define a univariate Gaussian Mixture Model (GMM) with two components, 5 parameters are needed: the mean and standard deviation for each component (4 in total), and the mixing coefficient for one of the components. Option D is correct.

Step-by-step explanation:

To fully define a univariate Gaussian Mixture Model (GMM) with two components, we need to determine several parameters. First, for each component, we need to know its mean and standard deviation, so that's two parameters per component.

Since we have two components, that gives us a total of 4 parameters for means and standard deviations (2 for the means and 2 for the standard deviations). Additionally, we also need to know the mixing coefficient for one component (the other can be derived as it must sum to one with the first), which is an additional parameter. Therefore, the total number of parameters required is 5:

Mean of the first component

Standard deviation of the first component

Mean of the second component

Standard deviation of the second component

Mixing coefficient for one of the components

In conclusion, the correct answer is D. 5.