This is a very tricky situation.
In general, new employees (at least in North America) are not entitled to any unofficial days off work unless there is a serious emergency or an immediate family member has just died. Unfortunately, the second anniverasry of your Father's death does not fall into the two exceptions that I previously described.
However; a lot has to do with the relationship between yourself and your manager. If the relationship is good, then I would suggest that you ask for a day off without pay. Notice that I used the term "ask". It's always better to speak in person with your manager than to write him a memo when it pertains to a personal issue.