Could someone explain the difference ?

In summary, explanation and clarification are both methods of providing information and understanding, but they differ in their approach. The decision to explain or clarify something depends on the level of understanding of the audience. An explanation can also serve as a clarification in some cases. While there is some overlap, teaching and explaining are not exactly the same. A clear explanation can improve understanding by breaking down complex concepts, providing context and examples, and addressing potential confusion or misconceptions.
  • #1
sneez
312
0
What is difference of probability density and probability distribution function?

If anyone has instructive example, i will appreciate it.

Thank u
 
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  • #2
Assuming the functions are nice, the density function is the derivative of the distribution function.
Example, uniform distribution between 0 and 1.
density function f(x)=1 for 0<=x<=1, =0, otherwise.
distribution function F(x)=0 for x<0, F(x)=x for 0<=x<=1, F(x)=1 for x>1.
 
  • #3


Probability density and probability distribution function are two concepts that are closely related and are often used interchangeably, but there is a subtle difference between them.

Probability density refers to the relative likelihood of a continuous random variable taking on a specific value. It is represented by a curve, with the area under the curve representing the probability of the variable taking on a range of values. The height of the curve at a specific point represents the probability density at that point.

On the other hand, a probability distribution function (also known as a probability mass function for discrete variables) gives the probability of a discrete random variable taking on a specific value. It is represented by a table, graph, or formula, where each possible value of the variable is assigned a probability.

In simpler terms, probability density is a continuous measure of probability, while probability distribution function is a discrete measure of probability. For example, the probability of a person's height being exactly 175 cm is represented by a probability density, while the probability of a person being exactly 175 cm tall is represented by a probability distribution function.

An instructive example of this difference can be seen in the normal distribution curve. The curve itself represents the probability density, while the specific values on the x-axis (such as the mean and standard deviation) can be used to calculate the probability distribution function for that particular normal distribution.

I hope this explanation helps to clarify the difference between probability density and probability distribution function.
 

1. What is the difference between explanation and clarification?

Explanation and clarification are both methods of providing information and understanding, but they differ in their approach. Explanation is the act of providing a detailed and comprehensive account of a concept or idea, while clarification is the act of making something clearer or easier to understand by providing additional information or context.

2. How do you know when to explain something and when to clarify it?

The decision to explain or clarify something depends on the level of understanding of the intended audience. If the audience is unfamiliar with the topic, it is best to provide an explanation to ensure they have a solid understanding. If the audience is already somewhat familiar with the topic, clarification can be used to fill in any gaps or address any confusion.

3. Can an explanation also be a clarification?

Yes, in some cases, an explanation can also serve as a clarification. This is often the case when an explanation is given to a specific question or misunderstanding, providing clarity on a particular aspect of a concept.

4. Is there a difference between explaining something and teaching it?

While there is some overlap between explaining and teaching, the two are not exactly the same. Teaching often involves a more structured and planned approach, with the goal of imparting knowledge and skills to the learner. Explanation, on the other hand, can occur in a more casual setting and may not necessarily involve teaching a specific skill or concept.

5. How can a clear explanation improve understanding?

A clear explanation can improve understanding by breaking down complex concepts into smaller, more digestible pieces. It can also provide context and examples to help the audience make connections and better retain the information. Additionally, a clear explanation can address any potential confusion or misconceptions, leading to a more accurate understanding of the topic.

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