DotKite said:Homework Statement
Let X and Y be rv's with joint pdf
f(x,y) = 6(1-y) for 0≤x≤y≤1 and 0 elsewhere
find Pr(X≤3/4, Y≤1/2)
Homework Equations
The Attempt at a Solution
Ok I am having trouble with finding the right limits of integration for dependent variables. If we let the inner integral be for x would the limits be 0 to y? Then would y be 1/2 to 1?
Jointly continuous random dependent variables refer to two or more random variables that are continuous (can take on any value within a range) and are related to each other in a way that their values are not independent of each other. This means that knowing the value of one variable can provide information about the values of the other variables.
Jointly continuous random dependent variables are different from independent variables in that their values are not independent of each other. Independent variables do not affect each other's values, while dependent variables do. This means that the relationship between jointly continuous random dependent variables is not simply due to chance.
The joint probability density function is a function that describes the probabilities of different combinations of values for two or more random variables. It is used to determine the probability of a particular outcome occurring for a set of dependent variables, taking into account their continuous nature and their relationship with each other.
Yes, jointly continuous random dependent variables can be correlated. Correlation refers to the strength and direction of the relationship between variables. In the case of dependent variables, correlation measures the strength and direction of the relationship between their values.
Jointly continuous random dependent variables are used in statistical analysis to model complex relationships between variables. They are often used in regression analysis, where one variable (the dependent variable) is predicted based on the values of one or more other variables (the independent variables). They are also used in multivariate analysis, where the relationships between multiple dependent variables are examined simultaneously.