Normal and lognormal distribution

[omgitsroy326]

Could someone explain to me the simple rules of adding subtracting multiplying dividing Normal and lognormal distributions?

My profs notes are very messy and it's really hard to keep up w/ also the supplied book was published in 1964 w/ no updates. Possibly a site?

I just need simple rules to follow which will make it easier for me to solve. thanks again

 

[omgitsroy326]

also how statistical independence plays a role in adding and subtracting two or more stdev and mean

 

[tacman]

The rules for adding, subtracting, multiplying, and dividing normal and lognormal distributions follow the same general rules as any other type of distribution. However, there are a few key differences to keep in mind when working with normal and lognormal distributions.

First, let's define what these distributions are. A normal distribution is a bell-shaped curve that is symmetrical around the mean, with the majority of the data falling within one standard deviation of the mean. A lognormal distribution is a skewed distribution where the logarithm of the data is normally distributed.

When adding or subtracting normal distributions, the resulting distribution will also be normal. The mean of the new distribution will be the sum or difference of the means of the original distributions, and the variance will be the sum of the variances. Similarly, when adding or subtracting lognormal distributions, the resulting distribution will also be lognormal. The mean and variance will follow the same rules as for normal distributions.

Multiplying or dividing normal distributions is a bit more complicated. When multiplying two normal distributions, the resulting distribution will not be normal. However, it can be approximated by a lognormal distribution. The mean of the new distribution will be the product of the means of the original distributions, and the variance will be the sum of the squared variances of the original distributions. Dividing two normal distributions will also result in a non-normal distribution, but it can be approximated by a lognormal distribution as well. The mean of the new distribution will be the quotient of the means of the original distributions, and the variance will be the sum of the squared variances of the original distributions, divided by the square of the mean of the denominator distribution.

In summary, the rules for adding, subtracting, multiplying, and dividing normal and lognormal distributions are similar to those for any other type of distribution, but there are some key differences to keep in mind. It is important to understand the properties of these distributions and how they behave when combined in order to accurately solve problems involving them. If you need additional help, there are many online resources available that provide explanations and examples of working with normal and lognormal distributions.