Random expenses are miscellaneous expenses. Not actually random, but they feel that way.
This is a jukugo word that uses the on'yomi readings of the kanji. You should be able to read this on your own. The ざつ goes to ざっ and the ひ goes to ぴ, making it into a dumb sounding word, like "zappy" (ざっぴ), so you can think about how some of your miscellaneous expenses were on zappy items.
What is the average cost of a Japanese college student’s food and miscellaneous expenses?