What is the best way to study for Exam P?

According to the previous post called Probability and Actuarial Science, actuaries are specially-trained professionals who use their knowledge of probability, statistics, and specific models to evaluate and price risks, e.g. risks of living too long, the risks of dying too soon, the risks of property damages, the risks of becoming sick and a whole host of other risks that are quantifiable. To be an actuary, a candidate must pass a series of exams.

It is fitting that the first actuarial exam, called Exam P, is on probability. How hard is Exam P? What is the pass rate? How much time should a student spend in studying for Exam P?

Exam P is administered by the Society of Actuaries (SOA). It is a 3-hour multiple choice exam consisting of 30 questions. There is a rule of thumb that says that the number of hours required for studying an actuarial exam is the length of the exam times 100. This would mean Exam P may requires 300 hours of studying and preparation.

The 300-hour requirement is not far fetched. Typically a student should take an undergraduate course in probability and statistics (calculus based) prior to taking Exam P. The class time for such as course can certainly be a part of the 300 hours.

Let’s say the class time is around 90 hours (spread over two 15-week semesters with 3 hours of class time each week). That leaves 210 hours for a period of intense studying prior to taking Exam P, sometime after taking the probability and stats course.

In fact, the most effective form of studying is working practice problems. In these 210 hours, the student should review concepts for sure. However, the best way to review is to apply what he or she has learned in the probability and stats course through problem solving.

Intense problem solving is not optional as the pass rate for Exam P and other actuarial exams tend to be around 40%. If a student spends 15 hours a week studying, the 210 hours of studying would take about 3 and a half months. Passing actuarial exams requires dedication.

We give another plug for our Exam P site. It has over 100 realistic Exam P practice problems. We know of students who passed Exam P as a result of studying our practice problems.

Dan Ma math

Daniel Ma mathematics

Dan Ma Exam P

Daniel Ma Exam P

Dan Ma actuarial

Daniel Ma actuarial

$\copyright$ 2018 – Dan Ma

Searching for hidden treasure

We want to talk about treasure hunt in mathematics. But first, focus on a treasure hunt that involves a treasure chest that is similar to the one shown above.

An ornate Romanesque 10-inch by 10-inch treasure chest weighing about 40 pounds that is filled with gold coins and other gems is “hidden in the Rocky Mountains, somewhere between Santa Fe and the Canadian border at an elevation above 5,000 feet. It’s not in a mine, a graveyard or near a structure,” according to Forrest Fenn, a millionaire art dealer in his 80s who lives in Sante Fe, New Mexico. His self-published memoir included a cryptic poem that describes the location of the treasure box.

TfhIeliw613FS.Rw$400pm (example found here). This is a 22-character password that is based on memorable phrase consisting of two sentences. The beauty is that the password has upper case and lower case letters and numeric characters and special symbols. It is arranged in such a way that people not in the know cannot guess easily. Of course, you who know the memorable phrase can remember. The same password should not be reused for other accounts (don’t be lazy). So come up with a memorable phrase for each account. There is another way to generate passwords that are strong. The passwords generated in this scheme are 26-character passwords with the first character being the first letter of the English alphabets, the second character being the second letter of the English alphabets and the third character being the third letter of the English alphabets and so on. In fact, this should be given in the Jimmy Kimmel’s video mentioned above. Though all the letters are known, the scheme produces over 67 million possible passwords (67,108,864 to be exact). Read this blog post to know more. Once someone understands how this scheme works, he or she understands the binomial distribution. $\text{ }$ $\text{ }$ $\text{ }$ $\copyright$ 2017 – Dan Ma Powerball and the lottery curse The recent winner of the Powerball jackpot is Mavis Wanczyk, a hospital worker from Chicopee, Massachusetts. The drawing was on 8/23/2017 and the winning numbers are 6, 7, 16, 23, 26, and Powerball number 4. The size of the jackpot was$758.7 million, the largest undivided lottery jackpot in North American history. Instead of having the winnings being paid out over a 30-year period (the annuity option), Wanczyk took a lump-sum payment of $480 million and took home$336 million after taxes. This recent winning is widely reported. Here’s are one instance and another instance of reporting.

We wish Ms. Wanczyk well, hoping that she will manage the unexpected windfall in ways that add to her happiness. For lottery winners of giant jackpot, sometimes the winning is the easy part. Google “the curse of the lottery”, you will see plenty of stories of lottery winners who lost big – breaking up of marriages, going bankrupt, getting robbed, being swindled and in some cases committing suicide or being murdered.

In some states, by law the lottery winners must make public appearances holding a giant publicity check in front of camera. For the states that have no such requirements, where the public appearances are voluntary, wise winners would skip any photo ops (their identity would still be revealed) and head immediately to an undisclosed location. They know that plenty of slings and arrows (in some cases bullets) would come their ways – from swindlers, fraudsters and robbers as well as from the long lost friends and relatives who want to share the wealth. Just like one famous line in the movie Forrest Gump, ‘run, Forrest, run!” That would be the best advice for a winner of a giant and sudden windfall of cash. Of course, it is also important to hire a reputable and trustworthy financial adviser.

Sudden windfall cash usually does not last long. About 70 percent of the time, the cash will be gone in a few years, according to the National Endowment for Financial Education (see this piece from time.com).

The Time piece also mentions several stories of lottery winnings gone wrong. One winner mentioned is Abraham Shakespeare, who won a $30 million jackpot in Florida. He told his brother, “‘I’d have been better off broke.” Shakespeare (the lottery winner) has his own page in Wikipedia. His eventual fate: he was murdered by a swindler named Dee-Dee Moore 3 years after winning the big prize. The Wikipedia page of Abraham Shakespeare is more like a posthumous monument of his notoriety as a murdered lottery winner, rather than for highlighting achievements. The Time piece also mentions a “success” story. Richard Lustig is a 65-year-old Florida man who is a seven-time lottery game grand-prize winner. He had the wisdom of hiring a good financial planner and a good accountant. With the right mindset and the foresight of financial planning, he and his family are enjoying the good life made possible by the lottery winnings two decades earlier. Shakespeare and Lustig are from two opposite extremes in post lottery winning experiences. In between these two extremes, there are plenty of nightmarish stories with most of them being ended up in poverty, some in drug addiction (stories are here and here). The Google search for “the curse of the lottery” turns up plenty of advice too. Here’s a piece from Forbes. Another article is a piece from Wired. The piece from Lotto Report has sad stories and other information that can shed more light on the lottery curse. Here’s home page of the Lotto Report. As horrendous as some of the lottery curse stories are, the odds of incurring such fate are extremely rare. The odds for winning the Mega Millions jackpot is 1 in over 175 million (see here for the calculation). The odds of winning the Powerball jackpot is one in over 292 million (see here for the calculation). The odds of being struck by lightning is 1 in 700,000 according to a piece from National Geographic (significantly below 1 in a million odds). The odds of lightning strike would be more similar to the odds for winning the jackpot in a smaller lottery, e.g. Fantasy 5 in California Lottery (1 in 575,757). Of course, the longer the odds, the larger the potential jackpot. In fact, some of the most viewed articles in a companion blog called Talking about Numbers are about lotteries. The articles deal with California Lottery. But the ideas and observations would apply to other lotteries as well. One way to calculate the odds of winning the top prize in a lottery is through math (done here for various games in California Lottery and here for Powerball). Another way is to look at data. In this piece in Talking about Numbers, I showed that there are only 257 winning tickets with payouts of$1 million or more in the 26-year period from 1985 (the founding of California Lottery) to August 2011, averaging 10 “$1 million plus” winning tickets a year. Of these 257 winning tickets, 247 are in the first 25 years and 10 in the last year. Naturally, I would like to update the study but California Lottery had since then made it hard to gather the data in their website. But the essential fact remains the same. There are on average about 10 winning tickets a year that pay out$1 million or more. These 257 winning tickets are out of over 9 billion purchased tickets! This means the odds for winning a “million dollar plus” prize in California prize are about one in 36 million (calculated here).

Of course, California Lottery will try their best to give the impression that winning is more commonplace. Lottery authorities are in the business of selling tickets. They do not want to provide a picture reflecting the true odds of winning big. The odds of 1 in 36 million are much better odds than the Powerball odds for sure. But the prizes are not as mega as Powerball (the average of 247 winning tickets from 1985 to 2010 for California Lottery is \$18 million).

This piece has more information on the study. Here’s another frequently viewed post on lottery topics.

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$\copyright$ 2017 – Dan Ma