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After completing this video you should be able to:
- Explain and calculate expected value and higher moments, mode, median, and percentile.
In this video, we will cover the concepts of normal and lognormal distributions and their key properties that are commonly tested in the SOA Exam P. By the end of this tutorial, you will be able to understand and calculate expected value, variance, higher moments, mode, median, and percentile for normal and lognormal random variables.
Firstly, we will introduce the normal distribution, which is a continuous probability distribution that has a bell-shaped curve. We will show how to define a normal random variable X ~ N(𝜇,𝜎^2), where 𝜇 is the mean and 𝜎^2 is the variance of the distribution. We will explain how to standardize a normal variable using the Z-score, which is defined as Z=(X-𝜇)/𝜎. Additionally, we will discuss how to calculate probabilities using the standard normal distribution table and how to use the central limit theorem to approximate normal distributions.
Secondly, we will cover the lognormal distribution, which is a continuous probability distribution that has a skewed-right shape. We will explain the relationship between the lognormal distribution and the normal distribution, where a lognormal variable X ~ LN(𝜇,𝜎^2) can be defined as X=e^Y, where Y ~ N(𝜇,𝜎^2). We will show how to calculate expected value, variance, and higher moments for a lognormal variable and how to transform a lognormal variable to a normal variable using the natural logarithm.
This video will help you gain a better understanding of normal and lognormal distributions and their key properties, which will help you prepare for the SOA Exam P. Don't forget to subscribe to our channel for more actuarial exam videos!
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