### Role of Generalised Linear Model in non-life pricing Phase3

Phase1: http://www.actuarysense.com/2018/10/role-of-generalised-linear-model-in-non.html
Phase2: http://www.actuarysense.com/2018/11/role-of-generalised-linear-model-in-non.html So we know that the purpose of GLM is to find the relationship between mean of the response variable and covariates.

Linear Predictor: Let’s denote it with, “η” (eta). So, linear predictor is actually a function of covariates. For example, in the normal linear model where function is Y = B0 + B1x. So linear predictor will be η = B0 + B1x. Always note that linear predictor has to be linear in its parameter. In this case parameters are B0 and B1. But still the question is how I came up with B0 + B1x as a function? First of all, note that broadly there are two types of Covariates. 1. Variables: It takes the numerical value. For example: age of policyholder, years of ex…

### Random Variable:

When there is a probability associated with a variable that makes it Random Variable.
So a Random variable can take many different values with different probabilities.

#### Example:

Q.1) No. of Days in a week-: Is this a Random Variable?

A.1)  NO, because no. of days in a week is fixed i.e 7

Q.2) No. of Days in a Month-: Is this a Random  Variable?

A.1)  Yes, because no. of days in a month can be 28,29,30 or 31. So this is Random in nature.

Note:

Suppose X is "Something" now it can take value "0" if 3 comes up on a Dice and "1" if even no. comes up on dice.

So we know that probability of getting a 3 on Dice is 1/6 . So probability of getting a value "0" is 1/6
Similarly the probability of getting an Even no. on dice is 1/2. So probability of getting "1" is 1/2.

so we see that when "something is attached with different values along with different probabilities it becomes a Random variable.