Distribution of a random variable , pdf vs probability distribution

This is because the distribution function can be defined for any random variable, while the density function only exists for continuous random variables. Therefore, the distribution function is a more general concept and can be used for both discrete and continuous random variables.
  • #1
cappadonza
27
0
Hey all i struggling to understand, these concepts. would some explain to me the relationship and differences the distribution of a random variable and a probabiltiy distribution.
wikipedia says this about probability distribution "The probability distribution describes the range of possible values that a random variable can attain and the probability that the value of the random variable is within any (measurable) subset of that range."

Now if you have probability mass funtion or density funtion which gives you the probability of a given set. why do we need a probability distribution funtion what does it buy us, it seems like they both giving us the same things

any help would me much appreciated
 
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  • #2
It is possible to have a probability distribution function which is not differentiable, so there will be no density function.
 

1. What is a random variable?

A random variable is a numerical quantity that is associated with a random event or experiment. It can take on different values based on the outcome of the event.

2. What is the difference between a PDF and a probability distribution?

A PDF (probability density function) is a mathematical function that describes the probability of a random variable taking on a specific value. A probability distribution, on the other hand, is a set of all possible values that a random variable can take on, along with their corresponding probabilities.

3. How is a PDF related to a probability distribution?

A PDF is derived from a probability distribution and provides a continuous representation of the probabilities associated with different values of a random variable.

4. Can a probability distribution be used for discrete and continuous random variables?

Yes, a probability distribution can be used for both discrete and continuous random variables. However, the types of probability distributions used may differ. For discrete random variables, probability mass functions are used, while for continuous random variables, probability density functions are used.

5. What is the importance of understanding the distribution of a random variable?

Understanding the distribution of a random variable is crucial in many fields of science and statistics. It allows us to make predictions and draw conclusions about the likelihood of certain events occurring. It also helps in making decisions and designing experiments in order to obtain more accurate results.

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