Limited Funds. Which C1 text?

[Packet_Storm]

Due to the fact that I have only work study as a job currently, (and car insurance payments). Which of the following text would you suggest to study for exam one.
Please note that I have already had an intro to statistic, and I am good at calculus; however, I don't know how to judge these books and need some imput. Thank you for your help.


Probability

† A First Course in Probability (Sixth Edition), 2001, by Ross, S.M., Chapters 1–8.
Fundamentals of Probability (Second Edition), 1999, by Ghahramani, S., Chapters 1–10.
Probability for Risk Management, 1999, by Hassett, M. and Stewart, D., Chapters 1–11.
Probability and Statistical Inference (Sixth Edition), 2001, by Hogg, R.V. and Tanis, E.A., Chapters 1–6.
† Probability: The Science of Uncertainty with Applications to Investments, Insurance and Engineering 2001, by Bean, M.A., Chapters 1–9.

-the list was taken from SOA website (http://www.soa.org/eande/spring02_catalog/spring02_course1.html)

[Macroman]

I would first see if you can find the reccommended texts in a library. If not the current editions then previous ones. If you are forced to go without some of the texts entirely (not a total disaster) I would probably lean toward a comprehensive study guide first (many actuarial students study entirely from study manuals) then possibly towards the more insurance specific titles from Hassett or Bean.

From the SOA web site:
The texts listed below are considered representative of the many texts used by colleges and universities in Canada and the US to cover material on which the candidate may be examined.
Earlier or later editions of the listed texts contain essentially the same material and should be adequate for review purposes. In addition there are study notes for this course. The candidate is
expected to be familiar with the concepts introduced in the study notes.

Translation: You can study from other materials for this exam.

Definitely, I would download all the past exams from the SOA web site

http://www.soa.org/eande/spring02_catalog/spring02_course1.html

[Packet_Storm]

I have download all the exams and answer sheets and have gotten Actex study guide. The books avaible at my local lib are either written in the 30-40's (and use drasticaly different language and symbols) and the one written in the 70's uses basic math.

I can get the book written by Bean from another libaray, but only for a short time. I have been looking for the answer books for any of the books listed which would help in checking the answers.

I can understand most of the tests, it the deals, for example question 1 on the Nov 2000 exam 1. Why does one square 1.2?

if the tax of 20% is across the board and the mean is 200 and var is 260, why square 1.2. to obtain the annual cost.

I understand y = 1.2X, and Var[y] = Var[1.2X], but I don't get (1.2)^2Var[X] = (1.2)^2(260) = 374.

It is the last step I have problem understanding. I know that Var is S.D.^2, but why must the tax be squared? Why isn't it just moved 20%?

This is why I would like a book, more than just Actex study guide. I can follow the study guide fairly well for what is written. I get the Calculus hands down, I just have to memorize some formula and I will be set on the Calculus. It is the deeper understanding of the Prob. I need.

[Gandalf]

I can understand most of the tests, it the deals, for example question 1 on the Nov 2000 exam 1. Why does one square 1.2?

if the tax of 20% is across the board and the mean is 200 and var is 260, why square 1.2. to obtain the annual cost.

I understand y = 1.2X, and Var[y] = Var[1.2X], but I don't get (1.2)^2Var[X] = (1.2)^2(260) = 374.

It is the last step I have problem understanding. I know that Var is S.D.^2, but why must the tax be squared? Why isn't it just moved 20%?


For any random variable Z, Var(Z) is defined as E[(Z-E(Z))^2]. In words, it's the average of the square of the distance from the values of Z to the mean.

In your problem, we've obtained Y from X by multiplying all values of X by 1.2. That process moves the points of Y are 1.2 times the distance from Y's mean that the corresponding points of X were from X's mean. When we square those distances, we get 1.44 times the original squared distances, and when we average the new squared distances we get 1.44 times the original average squared distance.

Since you know Var = S.D. ^ 2, you may be able to think of it as S.D. is multiplied by 1.2 (probably as intuitively sensible as Var being multiplied by 1.2) which leads to New Var = (new S.D.) ^ 2 = (1.2 old S.D.) ^ 2 = 1.44 * (old S.D. ^ 2) = 1.44 * Old Var.

[Macroman]

The rule VAR(aX) = a^2VAR(X) is a standard one you should memorize. For an explanation about why I reccommend Hogg and Craig's Mathematical Probability and Statistics work. I don't remember the exact title. I would be surprised if there is a University Library in the U.S. without access to this book. I don't think that the Hogg and Craig title on the current syllabus is comparable, but it may be a substitute.

You should look for tittles in Mathematical Statistics or Engineering Statistics, even titles from the 1930's may be more useful than the drivel written for today's psycology majors.

[J-Man]

First, as a psychologist I take offense. All kidding aside, don't go to a local public library. Try a University library. An older edition of Anton's calculus, or even Thomas, should work for calculus. For Math/Stat, I still use the 4th edition of Hogg and Craig, Introduction to Mathematical Statistics (which came out sometime in the 80s I think). Someone here has an older edition and it's just as good. Friendlier Stat books: Larsen/Marx or Hogg/Tanis. The thing about using Hogg and Craig is that you're really supposed to know the math. Although I think it is a great book, and is the one I always refer to, an easier book might be more useful for Course 1.

Best wishes and good luck!

[Rainbow Brite]

The Ross probability book was used in my university probability class (an upper level intro to prob). I'd say go to your local university bookstore and try and find it used. I still use it as a reference.

[Packet_Storm]

Thanks everyone for there input. Does anyone know if any of the prob. books have solution manuals to them?