for continuous distributions:
Recall for a joint distribution function ,
Law of Total Probability: Suppose and for , then for any event ,
In many cases, you will need to use the law of total probability in conjunction with Bayes Theorem to find or .
For a continuous distribution:
Effective study requires one to have clear goals in mind and to have a system by which to measure progress. Efficient study requires focus, attention and diligence throughout an entire study session. Complete coverage of all topics required for an exam takes dedication and hard work.
My study regiment so far has had none of these qualities. The goal of this blog will be to document my study behaviors in order to become a better actuarial student and increase my pass ratio.
The measurement of progress will be based on a point system as follows:
- 5 pts. — Completing a blog summary of a study session (I’m so lazy that this requires an award of points to serve as motivation)
- 5 pts. — Reading a page of the study manual
- 5 pts. — Reading a page of the textbook
- 10 pts. — Completing a study manual problem
- 15 pts. — Completing a practice exam problem
- 200 pts. — Completing a timed sample exam
My goal will be to try to achieve 50 to 100 pts. on weekdays and 100 to 150 pts. on weekends and holidays. The amount of study time per session will also be logged as a way to measure efficiency in pts/hr.