Learning a new language is always an exciting and daunting task; for me, Japanese was no exception. Although I do speak more than one language at a native level, I still knew that it would be a challenge to pick up a new language along with its writing system and grammatical structure. However, my love for Japanese culture, from the stunning landscapes to the unique cuisine and fascinating entertainment, pushed me to take on this challenge.

I was always intrigued by the language and how it was used in everyday life, from simple greetings to complex conversations. As someone who enjoyed watching Japanese anime and movies, I often wondered about the language and what it would be like to understand it better. I wanted to appreciate the nuances of the language and understand the culture on a deeper level. So, I decided to embark on a journey to learn Japanese and see where it would take me.

To start my journey, I chose to go with Duolingo. Duolingo is an innovative language-learning app that offers a fun and interactive way to learn a new language. I've been a Duolingo member for five years as of this writing, and it just seemed like an ideal starting place for me.

A key concept in the field of machine learning is that of uncertainty. It arises both through noise on measurements, as well as through the finite size of data sets. Probability theory provides a consistent framework for the quantification and manipulation of uncertainty and forms one of the central foundations for pattern recognition. When combined with decision theory, it allows us to make optimal predictions given all the information available to us, even though that information may be incomplete or ambiguous.

I will introduce the basic concepts of probability theory by considering a simple example. Imagine we have two boxes, one red and one blue, and in the red box we have 2 apples and 6 oranges, and in the blue box we have 3 apples and 1 orange as illustrated in the figure beside. Now suppose we randomly pick one of the boxes and from that box we randomly select an item of fruit, and having observed which sort of fruit it is we replace it in the box from which it came. We could imagine repeating this process many times. Let us suppose that in so doing we pick the red box 40% of the time and we pick the blue box 60% of the time, and that when we remove an item of fruit from a box we are equally likely to select any of the pieces of fruit in the box.