Lecture 3: Normal distribution

In today's lecture, we learnt three important properties of Normal distribution.

1. Sum of two independent normal random variables

2. Sum of n independent observations from the same Normal distribution

3. Multiple of Normal variables.

Remember the following rules:

• All the random variables must be independent.
• When two random variables are added or subtracted, their variance are always added.
• When a random variable is multiplied by a constant, say, a, the variance is multiplied by a^2.
• You can only add or multiply the variance, NOT the standard deviation.