Finding minimum variable's density function

In summary, the conversation discusses finding the density of Z, where X and Y are independent and each has a Uniform (0,10) distribution. The conversation includes discussing the cdf and the probability distribution of Z.
  • #1
wldnrp13579
3
0

Homework Statement


Let X and Y be independent and suppose that each has a Uniform (0,10) distribution.
Let Z = min{X, Y }. Find the density fZ(z) for Z.


Homework Equations





The Attempt at a Solution


i'm sorry but i really don't know how to handle this.
 
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  • #2
Start by finding the cdf.
 
  • #3
if x and y both have same uniform distribution, then z has the same distribution as x and y?
 
  • #4
wldnrp13579 said:
if x and y both have same uniform distribution, then z has the same distribution as x and y?

What are your reasons for thinking this? Have you actually computed the distribution?
 
  • #5
wldnrp13579 said:
if x and y both have same uniform distribution, then z has the same distribution as x and y?
FX(x) is the probability of what? Likewise, FZ(z).
 

1. What is a minimum variable's density function?

A minimum variable's density function is a mathematical function that represents the minimum possible value of a variable in a given set of data. It is often used in statistics and data analysis to determine the most likely value for a specific variable.

2. How is a minimum variable's density function calculated?

A minimum variable's density function is typically calculated using a statistical method, such as the maximum likelihood method. This involves finding the value of the variable that maximizes the likelihood of the observed data.

3. What is the purpose of finding a minimum variable's density function?

The purpose of finding a minimum variable's density function is to better understand the data and make predictions about future values of the variable. It can also be used to identify outliers or anomalies in the data.

4. How is a minimum variable's density function different from a probability distribution?

A minimum variable's density function is a specific type of probability distribution that represents the minimum possible value of a variable. It differs from other probability distributions in that it focuses on the minimum value rather than the entire range of values.

5. What are some real-world applications of a minimum variable's density function?

A minimum variable's density function is commonly used in fields such as finance, economics, and engineering to analyze data and make predictions. It can also be applied in areas such as risk management, market analysis, and quality control.

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