What are the incorrect limits on the integral in this random variables problem?

Thread starter vabamyyr
Start date Nov 24, 2005
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Random Random variables Variables

In summary, a random variable is a numerical value determined by chance or probability that represents the outcome of a random event or experiment. There are two types: discrete, which can only take on a finite or countably infinite number of values, and continuous, which can take on any value within a specific range. The expected value of a random variable can be calculated by multiplying each possible value by its corresponding probability and summing them up. Probability distributions are important in random variable problems as they describe the likelihood of each possible outcome and allow for predictions and informed decision-making. Random variables have various real-world applications, including in statistics, finance, and engineering, to model and analyze complex systems with uncertainty and randomness.

Nov 24, 2005

vabamyyr

Since I am noob in LaTex then ill post a document in Word.

Last edited: Nov 24, 2005

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Nov 24, 2005

mathman

Science Advisor

The limits on your integral are incorrect. You have to divide the x range into 2 parts (0,z) and (z,1). For the first part the y range is (0,1). For the second part the y range is (0,z/x). The point being that y has an upper limit of min(1,z/x).

1. What is a random variable?

A random variable is a numerical value that is determined by chance or probability. It represents the outcome of a random event or experiment and can take on various values with different probabilities.

2. What is the difference between a discrete and continuous random variable?

A discrete random variable can only take on a finite or countably infinite number of values, while a continuous random variable can take on any value within a specific range. For example, the number of heads in 10 coin flips would be a discrete random variable, while the height of a randomly selected person would be a continuous random variable.

3. How do you calculate the expected value of a random variable?

The expected value of a random variable is calculated by multiplying each possible value of the variable by its corresponding probability, and then summing up all of these products. It represents the average value that would be obtained if the experiment or event was repeated many times.

4. What is the importance of probability distributions in random variable problems?

Probability distributions describe the likelihood of each possible outcome of a random variable. They allow us to make predictions about the behavior of the variable and determine the probability of certain events occurring. In random variable problems, understanding the probability distribution is crucial for finding solutions and making informed decisions.

5. How are random variables used in real-world applications?

Random variables are used in many real-world applications, such as in statistics, finance, and engineering. They help to model and analyze complex systems and phenomena that involve uncertainty and randomness. For example, stock prices, weather patterns, and traffic flow can all be represented using random variables.