2 - Basic concepts of Probability

types of variables

• endogenous

• exogenous

depending on the problem a variable can change from endogenous to exogenous & vice versa

variable

something whose value can change either quantitatively or qualitatively

endogenous variable

dependent variable that moves passively or as a result of changes in another variable

exogenous variable

explanatory variable that moves actively or is the cause of changes in other variables

consumption function

Ct - endogenous

Yt - exogenous

alpha & beta - constants

consider demand curve

price determines quantity demanded, hence:

• Qdt - endogenous

• P - exogenous

inverse demand curve

arguably quantity demanded can determine price as well, meaning:

• Qdt - exogenous

• P - endogenous

  

random errors

systematic behaviour is likely to be affected by random errors

• these errors occur randomly and can only be known after the fact

• introduces randomness to the behaviour of endogenous variable, making it no longer perfectly predictable

consumption function with random errors

consumption is now random and not perfectly predictable because of random errors

• Ct is determined by both the systematic part and random errors

consumption function with random errors graphed

• red line - actual consumption

• black line - predicted consumption

• gaps - prediction errors/randomness

distribution of variables

variables follow a kind of distribution

distribution - described possible values a variable can take and the corresponding likelihood

values can be

• numerical

• non-numerical - i.e. head/tail of coin

• discrete - specific, distinct values

• discrete, numerical - outcome from rolling a die

• discrete, non-numerical - outcome from flipping a coin

• continuous - number of possible values is infinite

• continuous, numerical - possible temperature of Cardiff

distribution

distributions are formed by the number of observations

• summarises information about the variable:

  • probability/frequency - likelihood of observing

  • mean

  • volatility (variance)

probability

likelihood of observing a value or event based on the number of possible outcomes