What N ((1,0)T , I) mean related to Gaussian Distribution

Question

Hi everyone I am reading a book "Element of Statistical Learning) and came across the below paragraph which i dont I understand. (explains how the training data was generated)

We generated 10 means mk from a bivariate Gaussian distribution N((0,1)T,I) and labeled this class as blue. Similraly, 10 more were drawn from from N((0,1)T,I) and labeled class Orange. Then for each class we generated 100 observations as follows: for each observation, we picked an mk at random with probability 1/10, and then generated a N(mk, I/5), thus leading to a mixture of Gaussian cluster for each class.

I would appreciate if you could explain the above paragraph and especially N((0,1)T,I)

• by the way- (0,1) to the power of T for Transpose.
• Is this notation mathmatically common or related to a specific computer language.

Answer 1

In the paragraph N stands for the Normal distribution; more specifically, in this case it stands for the Multivariate normal distribution. It is not specific to any programming languages. It comes from statistics and probability theory, but due to numerous appealing properties and important applications of this probability distribution it is also widely used in programming, so you should be able to perform the described procedure in any language.

The part (0,1)^T is a vector of means. That is, we have in mind a random vector of length two, where the first element on average is 0, and the second one on average is 1.

"I" stands for the 2x2 identity matrix whose role is the variance-covariance matrix. That is, the variance of both random vector components is 1 (i.e., the diagonal terms), while off-diagonal points are 0 and correspond to the covariance between the two random variables.