# Tagged Questions

Actuarial science is a discipline that uses mathematics and statistics to assess risk. The mathematics involved in actuarial science includes probability, statistics, finance, life insurance mathematics, and more.

24k views

### How often does it happen that the oldest person alive dies?

Today, we are brought the sad news that Europe's oldest woman died. A little over a week ago the oldest person in the U.S. unfortunately died. Yesterday, the Netherlands' oldest man died peacefully. ...
1k views

### Calculating a continuously varying, continuously paid annuity

I'm unsure how to calculate a continuously varying, continuously paid annuity. I'll write up my solution (which I suspect is wrong) to one, sample question, and I would greatly appreciate any ...
151 views

### Prove that $\dfrac{0.5x^2 + x + 1}{x^2 + x + 1}$ is a strictly decreasing function.

This is part of an actuarial science problem. Unfortunately, the official solution of this problem takes the derivative of $$\dfrac{0.5x^2 + x + 1}{x^2 + x + 1}\text{, } \quad x \geq 0\text{.}$$ and ...
38k views

### Are the actuarial exams hard? [closed]

I heard that they are difficult. Is this true? Are they like the qualifying exams in grad school? For example, is the probability exam and the financial math exam comparable to qualifying exams (e.g. ...
2k views

### Which methods are used by actuaries in practice?

Recently I read a comment from an actuary that a lot of the math they studied as part of the program they never actually used. I'm not interested in becoming an actuary, but I'm interested in ...
3k views

### Masters in Actuarial Science

I am applying to a grad school for the Masters in Actuarial Science. Now i am getting cold feet. I do love math, i was always good in math (not excellent or a genius). Did all adv. calculus classes ...
332 views

### Claim from an Actuarial Textbook: limits imply the existence of mean and variance

This is from Actuarial Mathematics for Life Contingent Risks, 2nd ed., by Dickson et al. Some definitions (not directly from the book): Definitions/Notation. $T_x$ is defined to be the future ...
72 views

### Probability question : meaning of the sentence

The following is the problem I am working on. The probability of a passing car being an import is defined as $p(i)=1/4$ and the probability of it being domestic is $p(d)=3/4$. Find the probability ...
223 views

### Probability problem - fake and real diamonds -

A box contains 35 gems, of which 10 are real, 25 are fake. Gems are randomly taken out of the box, one at a time without replacement. What is the probability that exactly 2 fakes are selected before ...
269 views

5k views

### Confused about Effective Rate of Discount- Theory of Interest

I'm currently reading Kellison's book, The Theory of Interest. I've reached the chapter on Effective Rate of Discount and it's somewhat confusing. The book explains it as a loan where interest is paid ...
135 views

### Macaulay duration for a coupon bond. Proof

I am working on showing the following. There is a coupon bond redeemable at par with annual coupon rate $r$ per year. The yield to maturity is $i$. The total number of coupons is $n$. Show ...
267 views

### Beta distribution for exam P?

I had a quick question regarding the beta distribution and exam P for actuaries. From the recommended books that I have seem, beta distribution does not seem like it is likely to show up on the P ...
335 views

### Text on Probability Theory applied to Actuarial Science

I am a senior undergraduate who has passed the first three actuarial exams on probability (P), financial mathematics (FM), and models for financial economics (MFE). I am working on passing the life ...
993 views

217 views

### What is the best way to study Probability? [closed]

Nowadays, I am studying probability. I want to be an actuary and the first exam that I have to pass is P exam. I just want to know what is the best way and if you can recommend any books please let me ...
39 views

### Deriving a property regarding variance.

I am studying for the P-exam for actuaries and I've encountered a property that said, $Var(x\pm y)=Var(x)+Var(y)$ I come from a math major and it has been years since I was taught statistics or ...
116 views

### MGF, Calculate the standard deviation of $X + Y$ . Method.

Two claimants place calls simultaneously to an insurers claims call center. The times X and Y , in minutes, that elapse before the respective claimants get to speak with call center ...
484 views

### Remembering the mean and variance of Poisson vs Exponential

I am having the P-Exam for actuaries on September and I am trying to work on my details. One of the troubles that I have is to remember the difference between Poisson and Exponential distribution. I ...
84 views

### How is this the right answer?

In a survey of customer satisfaction, participants are asked to give a score of 1,2,3 or 4 to each of the 6 questions. If participants are instructed not to give the same numerical score to more than ...
41 views

415 views

### Pure Mathematics to Actuarial Science. [closed]

I did my undergraduate in pure mathematics and recently after a three year break I decided to get a master's degree in Actuarial Science. I am in the second week of classes and I feel completely lost. ...
893 views

### Darth Vader Rule: what is the reason for its name, and a formal proof?

I often hear the term "Darth Vader Rule" when calculating the expected value using the survival function and taking the integral where it is defined. I am not quite sure why it is called that (is it ...
90 views

### what is the formal mathematical relationship between the variance and the odds that the gambler who has smaller budget here?

Here is a part of Bob Anderson's answer in my question (Does variance do any good to gambling game makers?) Suppose you had two gamblers who were flipping coins against one another with fair odds ...
451 views

### Bonds and Force of Interest

Studying for FM/2 and ran into this problem dealing with bonds; A 1,000 par value 3 year bond with annual coupons of 50 for the first year, 70 for the second year, and 90 for the third year is bought ...
98 views

### How would I determine whether these events are independent?

I'm studying for CAS/SOA Exam 1/P and I'm stumped on this question. It says: From the set of families with two children a family is selected at random. Let $X_1=1$ if the first child of the family ...
995 views

### Converting an Annuity due to Annuity immediate

I'm working on the following problem at the moment while preparing for an exam. Find the present value of payments of 200 every six months starting immediately and continuing through four years from ...
62 views

### Eggs and Cranes, What is the probability that it is a whooping crane’s nest?

The problem said: In a certain region, blue cranes are twice as common as whooping cranes. Suppose that the number of eggs laid by a blue crane is a Poisson(! = 3) random variable and the ...