Bivariate probability distributions Flashcards
1
Q
What are the properties of the joint CDF
A
- it can be non decreasing
- as x and y both tend to infinity, the function tends to 1 and when it tends to - infinity it tends to 0
2
Q
For a pair of continuous random variables X and Y what is the join PDF
A
it is equal to the mixed second derivative of the joint CDF
3
Q
Every bivariate PMF is a non-negative function of 2 arguments, whose sum over the countable range spaces Rx and Ry is equal to 1.
A
4
Q
What is normalisation
A
The process of dividing the function g(x,y) by its sum or integral to turn it into a pdf or pdf
5
Q
What is the marginal cumulative distribution function of the random variable X?
A
Fx(X) = P(X <= x)
it is related to the regular function, when y tends to infinity
6
Q
what is the marginal pdf of Fx(X)
A
Fly(x,y) integrated between infinity and -infinity
7
Q
What is the marginal PMF of X given by?
A
the sum of Px,y(x,y)
8
Q
A
