Optimism from my point of view would be seeing the rational possibilitys and chosing to believe the one that you enjoy best will be the outcome of an event.

Where as I see hope as beliving something positive will come to be. But without rational thought behind it or beliving in something that is statistically impossible.

And example of Optimism is "If i save 50$ a month for 20 years that money and the intrest it collects should be enough to put my child through collage".

And an example of Hope would be "I sure hope that train sees me and decided to stop before it travels the extra 10 feet and hits me".