Lecture 2: Normal distribution

In this lecture, you have learnt the following points:

1. the use of " invNorm"

Example: X~ N(17,11), P(X is smaller than a ) =0. 38, use invNorm (0.38, 17, sqrt(11)) to find the value of a.

Note: If the given information is P(X is bigger than a)=0.38, you have change it to P(X is smaller than a)=1-0.38=0.62 before you use the "invNorm" function.

2. Properties of Normal distribution

If \[X\sim N(\mu ,\sigma ^{2}) \], \[aX+b \sim N(a\mu+b, a^{2}\sigma^{2})\]

3. Standard Normal distribution

• Standard Normal distribution is the normal distribution with mean 0 and variance 1.
• We can change any normal distribution to standard normal distribution. \[X\sim N(\mu ,\sigma ^{2}) \], \[\frac{X-\mu}{\sigma}\sim N(0,1)\]

You can make use the properties of Normal distribution to prove it.