Anne was optimistic that one day all their miseries would end.elucidate.

There are quite a few examples for this.

Even after describing how she cried upon leaving her Jewish Secondary school, she still says that "everything is all right."Saturday, 20 June, 1942

Anne makes the best of things, turning her tiny bedroom into a nice living space. Saturday, 11 July, 1942

A large bag of beans splits open, spilling 50 pounds. They all laugh at what happened and clean it up. Monday, 9 November, 1942

Anne understands how fortunate she and the others are inside the annexe. She is well aware of what is happening to her Jewish brothers and sisters outside in the "real" world. Friday, 20 November, 1942