normal-random | Generates normally distributed random variates

I have a copula representing the dependence between two variables X and Y. I want to compute the following formula: E(X|Y≤1%). It is the expected value of X conditional on Y being lower than 1%. I see that a somewhat similar question was asked there but the R code provided does not give the value I am looking for. Below are some details about the copula and marginal distribution.

I have been given a task of translating the simulations inside of the Excel plug-in @Risk to Python. The functionalities closely line up with numpy's random number simulation given a distribution type and mu, sigma, or high and low values. An example for what I am doing is here.

In the linked example, mu=2 and sigma=1. Using numpy I get the same distribution as @Risk.

I am curious as to how I can add a normal-randomized 300 dimension vector (elements' type = tf.float32) whenever a word unknown to the pre-trained vocabulary is encountered. I am using pre-trained GloVe word embeddings, but in some cases, I realize I encounter unknown words, and I want to create a normal-randomized word vector for this new found unknown word.

The problem is that with my current set up, I use tf.contrib.lookup.index_table_from_tensor to convert from words to integers based on the known vocabulary. This function can create new tokens and hash them for some predefined number of out of vocabulary words, but my embed will not contain an embedding for this new unknown hash value. I am uncertain if I can simply append a randomized embedding to the end of the embed list.

I also would like to do this in an efficient way, so pre-built tensorflow function or method involving tensorflow functions would probably be the most efficient. I define pre-known special tokens such as an end of sentence token and a default unknown as the empty string ("at index 0), but this is limited in its power to learn for various different unknown words. I currently use tf.nn.embedding_lookup() as the final embedding step.

I would like to be able to add new random 300d vectors for each unknown word in the training data, and I would also like to add pre-made random word vectors for any unknown tokens not seen in training that is possibly encountered during testing. What is the most efficient way of doing this?

How do we go about numerically solving equations of the sort below using R?

Please note, this can be shown to be convex and there is a separate thread on this. https://stats.stackexchange.com/questions/158042/convexity-of-function-of-pdf-and-cdf-of-standard-normal-random-variable

This question has been posted on the Mathematics Forum to get Closed Form or other Theoretical Approaches, but it seems numerically solutions are the way to go? https://math.stackexchange.com/questions/2689251/solving-equations-with-standard-normal-cdf-and-pdf-optimization