Probability / Probability density

In summary, the speaker asks if the probability of a particle being at a specific distance from its starting position is zero in a system where the particle can move in either direction with equal probability. The responder explains that in a continuous probability distribution, any specific value automatically has a probability of 0. The speaker clarifies that they do not have much knowledge about probability and mentions that this concept may be taught in quantum physics.
  • #1
Jelfish
144
5
Quick question:

I just started reading Feynman's Lectures and in one section (6-4) he says that for a system in which a particle (in 1 dimension) can move in either direction (with equal prob. of either direction). For each 'step' that the particle takes, the distance it moves can be any length such that the average length is, say, 1, then the probability of the particle being any specific distance away from its starting position is zero.

Is this because there are theoretically an infinite number of lengths that the particle can step, and thus the probability for any specific distance approaches 1/infinity?

(note - I haven't taken any quantum physics classes yet, which I imagine is where this stuff may be taught)
 
Physics news on Phys.org
  • #2
Your question is an elementary probability question (you don't need quantum physics). In the case described, the probability distribution is continuous, so that any specific value automatically has probability 0.
 
  • #3
I'm sure I don't know enough about probability as I should. I realize that this doesn't rely on any quantum physics. I was just mentioning that it seems like something that would show up more often there. Just wanted to make sure I understood it correctly. Thanks for your response.
 

1. What is the difference between probability and probability density?

Probability refers to the likelihood of a specific event occurring, while probability density is a measure of the likelihood of a continuous random variable taking on a specific value within a given range. In simpler terms, probability is used for discrete events, while probability density is used for continuous events.

2. How is probability calculated?

Probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. It is typically expressed as a fraction or decimal between 0 and 1, where 0 represents impossibility and 1 represents certainty.

3. Can probability be greater than 1?

No, probability cannot be greater than 1. A probability of 1 represents certainty, meaning the event is guaranteed to occur, while a probability greater than 1 would imply that the event is more than certain, which is not possible.

4. What is the difference between discrete and continuous probability distributions?

Discrete probability distributions are used for events that have a finite number of possible outcomes, such as rolling a die or flipping a coin. Continuous probability distributions are used for events that have an infinite number of possible outcomes, such as measuring the height of a person or the time it takes for a car to pass by.

5. How is probability density represented graphically?

Probability density is typically represented by a continuous curve in a graph, where the area under the curve represents the probability of a certain event occurring. The total area under the curve is always equal to 1, as it represents all possible outcomes.

Similar threads

I How can concentration gradient field come into existence immediately?
    • Other Physics Topics
Replies
0
Views
292
A Importance of Densities in QFT
    • Quantum Physics
Replies
1
Views
783
A combinatorial probability question
    • Precalculus Mathematics Homework Help
Replies
18
Views
447
MHB How to Calculate Probability of Visiting All Vertices in a Markov Chain?
    • Programming and Computer Science
Replies
1
Views
515
B Help with personal thoughts and observations in attempt to understand the fourth dimension better
    • Other Physics Topics
Replies
3
Views
649
A How to calculate Feynman amplitude in Fish diagram
    • High Energy, Nuclear, Particle Physics
Replies
2
Views
1K
A Calculating Probability of N Points on a Line Being Within Given Distance
    • Set Theory, Logic, Probability, Statistics
Replies
7
Views
2K
I Is "nondimensionalization" a misnomer?
    • Other Physics Topics
Replies
19
Views
1K
B Boltzmann factor interpretation
    • Other Physics Topics
Replies
1
Views
1K
I The interpretation of probability
    • Quantum Interpretations and Foundations
2
Replies
42
Views
5K

Hot Threads

Recent Insights

Back
Top