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- The concept of zero-probability event is used to determine which sets are negligible: if a set is included in a zero-probability event, then it is negligible.
www.statlect.com/fundamentals-of-probability/zero-probability-eventsZero-probability events | They are not impossible - Statlect
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Does a zero probability event mean an impossible event?
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Are all sample points a zero-probability event?
Mar 23, 2021 · This post in math stack exchange posts says why zero probability doesn't necessarily mean impossible events. Then why do we act like it is, in physics ,i.e., how is vanishing probability both necessary and sufficient for the impossibility of an event in physics?
No, there is zero probability (and thus no possiblity) of that event. Quantum mechanics does not allow for anything to happen. In fact, QM often specifies exactly what must happen in a given situation... that's why we use it!
- Definition
- Understanding The Example
- Almost Sure and Almost Surely
- Almost Sure Events
- Example of Almost Sure Event
- How to Cite
As we said, the definition is very simple. Despite the simplicity of the definition, there are some features of zero-probability events that might seem paradoxical.
The reason for the apparent paradoxes is that the sample space described above is uncountable. It has the power of the continuum. Sample spaces of this kind are very common in statistics. They implicitly arise every time that we define a continuous random variable. But why do we define mathematical objects that have such counterintuitive properties...
The notion of a zero-probability event plays a special role in probability theory and statistics because it underpins the important concepts of almost sure property and almost sure event. Often, we want to prove that some property is almost always satisfied, or something happens almost always. "Almost always" means that the property is satisfied fo...
Remember (see the lecture on probability) that some subsets of the sample space may not be considered events. The above definition of almost sure property allows us to consider also sets that are not, strictly speaking, events. However, in the case in which is an event, is called an almost sure event and we say that happens almost surely. Furthermo...
Consider the sample space and the assignment of probabilities introduced in the previous example: We want to prove that the eventis a zero-probability event. Since the set of rational numbers is countable and is a subset of the set of rational numbers, is countable. This implies that the elements of can be arranged into a sequence: Furthermore, can...
Please cite as: Taboga, Marco (2021). "Zero-probability events", Lectures on probability theory and mathematical statistics. Kindle Direct Publishing. Online appendix. https://www.statlect.com/fundamentals-of-probability/zero-probability-events.
What would we expect now for the distribution of distances $D$? What is, for example, the probability that $D=0$ after $30$ steps? The answer is zero! The probability is zero that $D$ will be any particular value, since there is no chance at all that the sum of the backward steps (of varying lengths) would exactly equal the sum of forward steps.
Mar 9, 2016 · But, a zero probability event does not mean an impossible event. The simplest example comes comes from a continuous model. Every point has zero probability but every point can be a possible...
Dec 20, 2011 · In summary, zero probability in the context of continuous variables and probability densities refers to an event that has a probability of zero, which means that the event is unlikely to occur. However, this does not mean that the event is impossible, as it is still possible to obtain a specific value within the continuous interval.
Nov 24, 2008 · No, we cannot calculate the probability of an event with zero probability. This is because the probability of an event is calculated by dividing the number of desired outcomes by the total number of possible outcomes, but if the desired outcome is impossible, there is no number to divide by.
