probability Archives - Infinity is Really Big

April 10, 2019April 23, 2019

Triangular Survival Models

Studying for Exam LTAM, Part 1.5

*An example of a triangular distribution probability density function (PDF).*

An important principle in mathematical modeling is to start simple. For example, if you have a situation where a linear function matches the trend in your data, go ahead and use a linear function rather than, for example, a quadratic function.

If a … Read the rest

April 9, 2019April 23, 2019

Constant Force of Mortality (Exponential Distribution)

Studying for Exam LTAM, Part 1.4

Survival random variables apply to other situations besides the lifetimes of people. A common example in textbooks is the lifetime of a light bulb.

Modern-day light bulb technology seems to be much better than it was even thirty years ago. I think this is especially true with regard … Read the rest

April 4, 2019April 23, 2019

The Complete Expectation of Life

Studying for Exam LTAM, Part 1.3

What is your life expectancy? Are you a smoker? A heavy drinker? Male or Female? And how well do you eat and exercise?

These factors can all affect how long you can “expect” to live.

However, the word “expect” can be misleading in this context. It is an … Read the rest

April 2, 2019April 23, 2019

The Force of Mortality (Hazard Rate Function)

Studying for Exam LTAM, Part 1.2

We all face potential risks to our lives every day. Daily risks include traffic accidents, lightening strikes, and poisoning. These risks can be quantified mathematically in numerous ways.

Fortunately, succumbing to a life-endangering risk on any given day has a low probability of occurrence. However, if you have … Read the rest

March 28, 2019March 28, 2019

Axiomatic Probability and Conditional Probability

New Videos: Videos #5 and #6 on Probability for Actuarial Exam 1/P

Mathematics is built on an axiomatic foundation. What does this mean? In a nutshell, it means that every topic in mathematics is based on both undefined terms and on statements that are assumed to be true.

Upon hearing this, many people wonder “how can this be … Read the rest

March 25, 2019March 28, 2019

Studying for Exam LTAM Series

My Background and Your Prerequisites

This post is the first in a series about studying for Actuarial Exam LTAM — Long-Term Actuarial Mathematics. This exam is basically equivalent to the exam previously labeled Exam MLC — Models for Life Contingencies.

Back in the year 2005, I studied for and passed actuarial Exams P and FM (Exams 1 and 2), on … Read the rest

March 22, 2019March 25, 2019

De Morgan’s Laws and Commutative Diagrams

New Videos: Videos #3 and #4 on Probability for Actuarial Exam 1/P

As I emphasized in my most recent post “Venn Diagrams and Probability Notation“, simple probability problems are often best solved with pictures and basic logic, but more complicated problems may require formulas.

We are definitely not at the point in my video series where more complicated … Read the rest

March 20, 2019October 30, 2019

Venn Diagrams and Probability Notation

New Videos: Videos #1 and #2 on Probability for Actuarial Exam 1/P

Visualizing probabilities as areas in a Venn diagram.

Sometimes people think that fancy notation and formulas must always be relied upon to solve probability problems. This is definitely not the case, however. Sometimes visuals, such a Venn diagrams, are good enough to help you get the

… Read the rest