- #1
mnf
- 4
- 0
if the joint p.d.f of x,y is given by
f(x,y)= a |x-y| ,0<=x,y<=1
f(x,y)= 0 , o.w
find i)a
ii)p(y>x)
iii)p(x=y)
f(x,y)= a |x-y| ,0<=x,y<=1
f(x,y)= 0 , o.w
find i)a
ii)p(y>x)
iii)p(x=y)
a must be such that the total probability is 1. [itex]x\ge y[/itex], and so |x-y|= x- y, for (x,y) on the triangle with vertices at (0,0), (1, 1), and (1, 0). [itex]y\ge x[/itex], and so |x- y|= y- x for (x,y) on the triangle with vertices at (0, 0), (1, 1), and (0, 1). That is, we must havemnf said:if the joint p.d.f of x,y is given by
f(x,y)= a |x-y| ,0<=x,y<=1
f(x,y)= 0 , o.w
find i)a
Again, y> x in the triangle with vertices at (0,0), (1, 1), and (, 1).ii)p(y>x)
Any double integral over a line is 0.iii)p(x=y)
A joint distribution is a statistical concept that describes the probability of two or more random variables occurring together. It shows how the values of these variables are related and can be used to analyze and make predictions about data.
A marginal distribution is a probability distribution of a single variable, while a joint distribution considers multiple variables. In other words, a joint distribution provides information about two or more variables together, while a marginal distribution only focuses on one variable.
A joint distribution allows us to understand the relationship between two or more variables, and how they affect each other. It can help us identify patterns and make predictions about future events based on the data.
A joint distribution is calculated by multiplying the probabilities of each individual event occurring together. For example, if we have two variables A and B, the joint probability of A and B occurring together is equal to P(A) * P(B).
Yes, a joint distribution can be used for continuous variables. In this case, it is represented by a joint probability density function instead of a probability mass function. The principles of calculating a joint distribution for continuous variables are the same as for discrete variables.