What is the Density of the Quotient of Two Independent Random Variables?

In summary, the problem is to calculate a density function for Y/(X+1), given that X and Y are independent random variables with specific densities. There are various methods that can be used, such as change of variable and convolution, but it is not clear which method is most appropriate for this specific problem. Further exploration and manipulation of the equations may be necessary to find a solution.
  • #1
bsmith2000
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Homework Statement



Say X and Y are independent random variables with densities f and g, respectively:

f(x) = e^(-x) if x > 0 and 0 if x < 0

g(y) = 2e^(-2y) if y > 0 and 0 if y < 0

Calculate a density function for Y/(X+1)

Homework Equations


Change of variable?
Convolution?
Calculating distribution function?

The Attempt at a Solution



I know convolution let's you find the addition of densities, but dividing them is something altogether new for me, and I am not sure how to even approach it.
 
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  • #2
I am thinking the change of variable method, but I'm not sure how to manipulate it to solve this problem.
 

FAQ: What is the Density of the Quotient of Two Independent Random Variables?

What is the definition of density of two functions?

The density of two functions is a mathematical concept that measures the concentration of the values of two functions in a given interval. It is calculated by dividing the difference between the two functions by the length of the interval.

How is density of two functions different from density of one function?

Density of one function measures the concentration of values of a single function in a given interval, while density of two functions measures the concentration of values of two functions in the same interval. It takes into account the difference between the two functions.

What is the significance of density of two functions in real-life applications?

Density of two functions is commonly used in statistics and data analysis to compare the distribution of two variables. It can also be used in economics to measure the relationship between two economic variables.

How is density of two functions calculated?

The density of two functions is calculated by finding the difference between the two functions over a given interval, and then dividing that difference by the length of the interval. The result is a measure of the concentration of the two functions in that interval.

Can the density of two functions be negative?

Yes, the density of two functions can be negative if the values of the two functions are decreasing in the given interval. This indicates a higher concentration of values towards the end of the interval as compared to the beginning.

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