I think equation 4 is just derived from equation 3. The top bit counts every time before that y_i has taken a particular value y, and multiplies it by the dista

I think equation 4 is just derived from equation 3. The top bit counts every time before that y_i has taken a particular value y, and multiplies it by the distance of the x value then, x_i, from the value of x now. (Squared and exponentiated because this is the pdf of the normal distribution.) Here's an interpretation: if there were no noise, you might just count the number of times x took on a particular value and y took on a particular value, and divide that by the total number of times x took on that value. This would give you an empirical estimate of the prob of y given x. Because there's noise, they weight the counts by the pdf of the normal distribution of x - x_i. So, whenever x_i was close to current x, and y_i was a given y, that increases the probability of y occuring now.