Continuous Random Variables

In summary, an ambulance traveling at a constant speed along a road of length L has an accident occur at a point that is uniformly distributed on the road. The ambulance's location at the moment of the accident is also uniformly distributed. Using the ambulance position (X) and accident position (Y), the distribution of the ambulance's distance from the accident can be found by computing fx(x) = 1/L for x<=L and fy(y) = 1/L for y<=L. Further steps are needed to find f|x-y|(x-y).
  • #1
dashkin111
47
0

Homework Statement


An ambulance travels back and forth, at a constant speed, along a road of length
L. At a certain moment of time an accident occurs at a point uniformly distributed on the
road. (That is, its distance from one of the fixed ends of the road is uniformly distributed
over (0,L).) Assuming that the ambulance's location at the moment of the accident is also
uniformly distributed, compute, assuming independence, the distribution of its distance from
the accident.


Homework Equations





The Attempt at a Solution



Using X = ambulance position, Y = accident position I found

fx(x) = 1/L for x<= L
fy(y) = 1/L for y<=L

Now I'm stuck. :(
 
Physics news on Phys.org
  • #2
So am I right thinking we have to find:

f|x-y|(x-y)?
 
  • #3
Last bump, I hope someone can help me this time!
 

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

A discrete random variable can only take on a finite or countably infinite set of values, while a continuous random variable can take on any value within a certain range.

2. How are continuous random variables represented mathematically?

Continuous random variables are typically represented by a probability density function (PDF), which describes the probability of the variable taking on a certain value within a given range.

3. What is the relationship between the PDF and the cumulative distribution function (CDF) for a continuous random variable?

The CDF is the integral of the PDF over a certain range, and it gives the probability that the variable will take on a value less than or equal to a specific value.

4. Can a continuous random variable take on a value of exactly zero?

No, the probability of a continuous random variable taking on any specific value is zero. This is because the range of values is infinite and the probability is spread out over this infinite range.

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

Continuous random variables are used in various fields, such as finance, engineering, and physics, to model and analyze real-world phenomena that involve a range of possible values. For example, stock prices, weather patterns, and particle movement can all be modeled using continuous random variables.

Similar threads

  • Calculus and Beyond Homework Help
Replies
2
Views
1K
  • Calculus and Beyond Homework Help
Replies
9
Views
2K
  • Calculus and Beyond Homework Help
Replies
5
Views
1K
  • Calculus and Beyond Homework Help
Replies
8
Views
1K
  • Calculus and Beyond Homework Help
Replies
1
Views
691
  • Calculus and Beyond Homework Help
Replies
7
Views
1K
  • Calculus and Beyond Homework Help
Replies
4
Views
2K
  • Set Theory, Logic, Probability, Statistics
Replies
30
Views
2K
  • Calculus and Beyond Homework Help
Replies
13
Views
11K
  • Math POTW for Graduate Students
Replies
3
Views
983
Back
Top