In many statements in probability, there is an assumption like bounded

Thread starter forumfann
Start date Jan 7, 2010
Tags

Bounded Probability

In summary, when a statement in probability is said to be bounded, it means that there is a limit or restriction on the possible outcomes of the event being studied. This assumption can have a significant impact on probability calculations, allowing for the use of certain probability distributions and preventing the probability from exceeding a value of 1. However, not all statements in probability are assumed to be bounded, as some events may have infinite or unbounded outcomes. Examples of bounded events in probability include coin tosses, dice rolls, and the outcomes of a standard deck of cards. Common misconceptions about the assumption of boundedness include thinking it only applies to discrete events and assuming a probability of 0 or 1 automatically means the event is bounded. It is important

Jan 7, 2010

forumfann

In many statements in probability, there is an assumption like bounded fourth moment, so is there any random variable which has unbounded fourth moment?

Physics news on Phys.org

Jan 7, 2010

bpet

Some heavy-tailed distributions such as Cauchy & Pareto distributions have infinite moments.

1. What does it mean for a statement in probability to be bounded?

When a statement in probability is said to be bounded, it means that there is a limit or restriction on the possible outcomes of the event being studied. This can also refer to the range of values that the probability can take on, which is typically between 0 and 1.

2. How does the assumption of boundedness affect probability calculations?

The assumption of boundedness can have a significant impact on probability calculations. It allows for the use of certain probability distributions and mathematical models that are specifically designed for bounded events. It also helps to prevent the probability from exceeding a value of 1, which is not possible.

3. Are all statements in probability assumed to be bounded?

No, not all statements in probability are assumed to be bounded. Some events or situations may have infinite or unbounded outcomes, such as the time it takes for a particle to decay. In these cases, the assumption of boundedness may not apply and different probability methods may need to be used.

4. What are some examples of bounded events in probability?

Some examples of bounded events in probability include coin tosses, dice rolls, and the outcomes of a standard deck of cards. These events have a finite number of possible outcomes and the probability can be calculated using the assumption of boundedness.

5. What are some common misconceptions about the assumption of boundedness in probability?

One common misconception is that the assumption of boundedness only applies to discrete events. However, it can also apply to continuous events, as long as there is a limit or restriction on the range of possible outcomes. Another misconception is that a probability of 0 or 1 automatically means that the event is bounded, but this is not always the case. It is important to carefully consider the assumptions and limitations when using the concept of boundedness in probability.