A Markov chain is a discrete random process with the property that the next state depends only on the current state (wikipedia). A Markov chain is a discrete random process with the property that the next state depends only on the current state (wikipedia). So $P(X_n | X_1, X_2, \ldots X_n-1) = P(X_n | X_{n-1})$.
Some people find molecules and compounds confusing. Here's how to remember the difference. If you join two different chemical elements together, you can often make a completely new substance. Glue two atoms of hydrogen to an atom of oxygen and you'll make a single molecule of water.
A molecule is what you get when any atoms join together. A compound is what you get when atoms of two or more different elements join together. All compounds are molecules, but not all molecules are compounds. Water is a molecule because it is made from atoms that have been chemically combined. It is also a compound because the atoms that make water are not all the same-some are oxygen and some are hydrogen. Oxygen in the atmosphere is a molecule because it is made from two atoms of oxygen. It is not a compound because it is made from atoms of only one element-oxygen. This type of molecule is called a diatomic molecule, a molecule made from two atoms of the same type.