Econometrics 1: A Review of Statistical Concepts 1.1 - Random Variables, Distribution and Density Functions Flashcards
What type of variables are usually dealt with in Econometrics?
Random continuous variables
What are the names of the graphs that depict the probabilities associated with the values taken by random variables
Density & distribution functions
What do density & distribution functions do?
They depict the probabilities associated with the values taken by random variables
Describe the density function of a random variable
The density function of a random variable π is often
denoted π(π₯). The x-axis, βXβ, represents the continuous range of values over which the random variable π exists and
the y-axis, βf(x)β, is the value of the density function. The probabilities associated with variable π are
measured by areas under the density function (under the curve). So, for example, the probability
that the value of π will be between the values π and π is equal to the value ofβ¦ letβs say area π΄, i.e. Area π΄
π(π < π < π) = β«with upper limit of a and lower limit of b π(π₯)ππ₯. Hence calculating probabilities from density functions requires
integration. A feature of random variables and their densities is that the area under the whole density is equal
to unity, i.e. β« with upper limit of β and lower limit of -β π(π₯)ππ₯ = 1. Why is this? Letβs suppose that the variable can only take on values in the range 0 to 10. Then the probability of the variable taking on a value between 0 and 10 has to
be 1 and therefore β« with upper limit of 10 and lower limit of 0 π(π₯)ππ₯ = 1