Graphing density probability functions

In summary, the problem involves finding the joint probability density function for Y1 and Y2, which is given by 8y1y2^2 over the region of 0<=y1<=1, 0<=y2<=1, and y1^2<=y2. The attempt at a solution involved trying to graph the function in a square region and determining its independence, but it is unclear how to properly graph multi-variable functions in probability. The end goal is to find the integral of the function over the given region, which should equal 1.
  • #1
RET80
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Homework Statement


let Y1 and Y2 have the joint probability density function given by:
8y1y22, 0 <= y1 <= 1, 0 <= y2 <= 1, y12 <= y2

0, otherwise



Homework Equations


Basic integrals? if they are even needed.


The Attempt at a Solution


I attempted it, by assuming 0 - 1 for y1 and y2 and got a square from 1 to 1 on y1 to y2

But assuming it's a square, it must be independent, and I continued the work and it is NOT independent, so the square shape would be wrong?

I'm not too sure on how to graph multi-variable functions like this in probability.
 
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  • #2
It's only the part of the square where (y1)^2<=y2. You didn't say what the problem is, but I think you just want to show the integral of 8*y1*y2^2 over that region is 1, right? Can you show us how you tried to do that?
 

FAQ: Graphing density probability functions

1. What is a density probability function?

A density probability function, also known as a probability density function or PDF, is a mathematical representation of the likelihood that a random variable will take on a certain value. It is used to describe the probability distribution of a continuous random variable.

2. How is a density probability function graphed?

A density probability function is typically graphed as a curve on a coordinate plane, with the x-axis representing the possible values of the random variable and the y-axis representing the probability of each value occurring. The curve is usually smooth and can take on a variety of shapes, such as bell-shaped, uniform, or skewed.

3. What information can be obtained from a density probability function graph?

A density probability function graph can provide information about the likelihood of a random variable taking on certain values. The area under the curve represents the total probability of all possible outcomes, and specific values on the x-axis can be used to calculate the probability of those values occurring.

4. How is the area under a density probability function curve related to probability?

The area under a density probability function curve represents the total probability of all possible outcomes. This means that the probability of a random variable falling within a certain range of values on the x-axis can be determined by finding the area under the curve within that range.

5. What are some common applications of density probability functions?

Density probability functions are commonly used in statistics, data analysis, and various fields of science to model and analyze continuous random variables. They are also used to make predictions and decisions based on probability, such as in risk assessment and financial modeling.

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