Understanding Uniformly Distributed Random Variables

P ~ U(1,2) also, or if the range changes.In summary, the conversation discusses the probability distribution of a random variable P ~ U(1,2) and the possibility of a new random variable xP ~ U(1,2). It is determined that if x > 0, then the probability distribution for xP is still a Uniform Distribution with a range of (1,2). The conversation also mentions the assumption that U(1,2) is the uniform distribution on (1,2) and the potential distribution of xP being U(x,2x).
  • #1
roadworx
21
0
If I have random variable, P ~ U(1,2), am I correct in thinking that xP ~ U(1,2) also ? (where x is some constant), or does the range change?

Thanks.
 
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  • #2
Since P is U(1, 2), Prob(P < p) = p - 1. Note Prob(P < 1) = 1 - 1 = 0 and Prob(P < 2) = 2 - 1 = 1.

Assume x > 0, then Prob(xP < p) = Prob(P < p/x) = ...

Does this help?
 
Last edited:
  • #3
EnumaElish said:
Since P is U(1, 2), Prob(P < p) = p - 1. Note Prob(P < 1) = 1 - 1 = 0 and Prob(P < 2) = 2 - 1 = 1.

Assume x > 0, then Prob(xP < p) = Prob(P < p/x) = ...

Does this help?

So Prob(P<p/x) = p/x -1 ?

when p=x Prob = 0, and 2p = x, Prob = 1

So xP still follows a Uniform Distribution ~ U(1, 2).

It looks as though I've assumed this though.
 
  • #4
if U(1,2) is the uniform distribution on (1,2), then the random variable xP would be distributed according to U(x,2x).

Torquil
 
  • #5


I can confirm that your thinking is correct. When a random variable P is uniformly distributed between 1 and 2, any multiple of P, such as xP, will also be uniformly distributed between 1 and 2. This is because the multiplication by a constant does not change the range of the distribution. However, the mean and variance of xP will be different from P, as they are affected by the constant x. So while the range remains the same, the distribution of xP may have different characteristics. I hope this clarifies your understanding.
 

1. What is a random variable?

A random variable is a numerical value that is determined by chance. It can take on different values depending on the outcome of a random event or experiment.

2. How is a random variable different from a regular variable?

A random variable is different from a regular variable because its value is not known or determined beforehand. It is based on the outcome of a random event, while a regular variable is assigned a specific value.

3. What is the purpose of using random variables in research?

Random variables are used in research to model and analyze random events or experiments. They allow researchers to make predictions and draw conclusions based on probability and statistical analysis.

4. What are the types of random variables?

There are two types of random variables: discrete and continuous. Discrete random variables can only take on a finite or countable number of values, while continuous random variables can take on any value within a given range.

5. 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 by its corresponding probability, and then summing all of these products. It represents the average value or outcome that can be expected from the random variable.

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