Bivariate Probability question

In summary, to find the probability P(x<=3/4, y>=1/2), you need to draw the area where f(x,y) is non-zero, as well as the regions x<=3/4 and y>=1/2 on the x y plane. Then, set up a double integral of f(x,y) over the required region to find the desired probability.
  • #1
fireb
11
0

Homework Statement


Let x and y have the join probability density function given by

f(x,y) = 6 (1-y) 0<= x<=y<= 1
= 0 elsewhere
Find P(x<=3/4, y=> 1/2)


Homework Equations





The Attempt at a Solution



I know you have to find the probability in 2 parts.. but i am unsure how to do it?? any advice will be appreciated, thanks in advice.
 
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  • #2
start by drawing the following in the x y plane
- the area where f(x,y) is non-zero
- the region x<= 3/4
- the region y >= 1/2

the use this information to set up a double integral of f(x,y) over the required region
 

1. What is bivariate probability?

Bivariate probability is the probability of two events occurring simultaneously or the probability of one event occurring given that another event has already occurred. It involves analyzing the relationship between two variables and their likelihood of occurring together.

2. How is bivariate probability calculated?

Bivariate probability is calculated by dividing the number of times the two events occur together by the total number of observations. This can also be expressed as the joint probability of the two events.

3. What is the difference between bivariate and univariate probability?

Bivariate probability involves analyzing the relationship between two variables, while univariate probability focuses on the probability of a single event occurring.

4. What is the importance of bivariate probability in scientific research?

Bivariate probability is important in scientific research because it allows for the analysis of the relationship between two variables, which can provide insights and help in making predictions. It is commonly used in fields such as statistics, psychology, and economics.

5. Can bivariate probability be used to prove causation?

No, bivariate probability alone cannot prove causation between two variables. While it can show a relationship between them, further research and evidence is needed to establish causation.

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