# Epsilon from Bivariate Normal Distribution [duplicate]

I came across the following example from a book. I am given a dataset generated from a bivariate normal distribution:

Among the data, there are missing values for the last 20 of x2i (but not for x1i). The example demonstrates how EM algorithm comes into play to impute the missing value. The procedures are attached below:

It is further commented that the E-step conditional expectation is derived from the following formula:

I don't understand how this formula (the one with epsilon) is derived. Could anyone give me a reference for that?

## marked as duplicate by whuber♦Dec 13 '18 at 17:30

• The quotation is puzzling because you show us equation $(4.1)$ but the explanation refers to equation $(4.3)$ which isn't shown. To give you a useful answer, we need definitions of all variables and all distributional assumptions that are being made. – whuber Dec 13 '18 at 17:10