Both adjectives refer to things done or occurring without a definite aim, reason, or pattern. Random suggests something occurring by chance or accident (random thoughts, random acts of violence, a random assortment). A random event has as much chance of happening as any other thing like it. There is no more reason for something arbitrary than there is for something random, but arbitrary implies something done by whim or personal preference rather than according to some discernible logic or rationale (listed in an arbitrary order, an arbitrary decision, an arbitrary deadline). For this reason, arbitrary can suggest unreasonableness, irrationality, and even injustice. These connotations, however, come more from the other, earlier definitions of arbitrary, which refer to a decision made by an individual judge or arbiter rather than by following the law.
Enthusiastic and avid both refer to having or showing an energetic interest in something or an eager willingness. Enthusiastic, the more common word, has a wider range of application than avid. It implies spirited interest, motivation, or approval, and often involves an outward demonstration of these states (an enthusiastic reaction). Avid suggests a sort of hungry eagerness and sustained or committed interest, usually in the pursuit of an activity, especially a hobby (an avid reader, an avid snowboarder, an avid fan). Avid describes a quality of the pursuit, as much as or more than the state or attitude of a person—we don’t say someone is avid about snowboarding. However, in a much less common sense of avid, people can be said to be avid for, that is, eagerly desirous of, something anticipated (readers avid for the author’s next book).
Stubborn and obstinate imply resistance to advice, objection, pleading, or force. Both words are frequently found paired with refusal and resistance (obstinate resistance to change), and stubborn people can be as frustratingly unyielding as obstinate people. At the same time, the word stubborn might convey admirable qualities such as perseverance and determination, whereas obstinate can carry more negative connotations of a harmful rigidity, arrogance, or perversity. The obstinate are more likely to dig in their heels on the wrong side of an issue (obstinate refusal to admit his error). Typical adverbs used to characterize obstinate include incorrigibly and arrogantly.