Interpret Probability Distribution: Discrete Probability

  • Thread starter hoffmann
  • Start date
  • Tags
    Discrete
In summary, the given probability distribution involves a summation of a binomial coefficient, representing the number of successes out of k trials, multiplied by the probability of success and failure. When simplified, it resembles a negative binomial distribution with the number of successes divided by r. This can also be seen as the expected value of a geometric distribution. However, it is not possible to draw conclusions about the relationship between the two distributions using this formula.
  • #1
hoffmann
70
0
how do i interpret this probability distribution:

[tex]\sum_{k=r}^\infty \binom{k}{r}p^k(1-p)^{k-r}[/tex]

where r is the number of successes, p is the probability, k trials.

by looking at it, it seems like it's similar to a negative binomial distribution once you pull out a k/r. if you do some math after pulling out the k/r, it seems like it is the expected value of a geometric distribution. is this distribution saying that a negative binomial divided by the number of successes r means there is only one success, which is geometric?
 
Physics news on Phys.org
  • #2
in other words, what does this sum equal?
 
  • #3
hoffmann said:
how do i interpret this probability distribution ... it seems like it's similar to a negative binomial distribution once you pull out a k/r

Do you mean to ask "what is a probabilistic interpretation of this summation formula?" - in which case there would be lots of different ways to write it as an expected value E[f(X)] = sum(f(k)*Prob[X=k]). One way you found was with negative binomial X and f(X)=X/r; the other way was E[g(Y)] for some function g where Y is geometric.

However it sounds like you want to use E[f(X)]=E[g(Y)] to draw conclusions about how X and Y are related, but that's just not possible.

Does that help?
 
  • #4
makes sense. thanks!
 

1. What is a discrete probability distribution?

A discrete probability distribution is a statistical function that assigns a probability to each possible value of a discrete random variable. It is often represented in the form of a table or graph, where the sum of all probabilities is equal to 1.

2. How is a discrete probability distribution different from a continuous probability distribution?

A discrete probability distribution deals with discrete random variables, which can only take on a finite or countably infinite number of values. In contrast, a continuous probability distribution deals with continuous random variables, which can take on any value within a given range.

3. How do you interpret a discrete probability distribution?

To interpret a discrete probability distribution, you need to understand the probability assigned to each possible value of the random variable. This can be done by looking at the values on the x-axis of the distribution graph, which represent the possible outcomes, and the corresponding probabilities on the y-axis.

4. What is the relationship between a probability distribution and a probability mass function?

A probability mass function is a mathematical function that defines the probability of a discrete random variable taking on a specific value. It is used to calculate the probabilities in a discrete probability distribution by plugging in the values of the random variable.

5. How can a discrete probability distribution be used in real life?

Discrete probability distributions can be used in various real-life situations, such as in predicting the outcome of a coin toss, the number of customers at a store, or the number of defects in a product. They can also be used in decision-making processes, risk analysis, and quality control.

Similar threads

  • Set Theory, Logic, Probability, Statistics
Replies
3
Views
1K
  • Set Theory, Logic, Probability, Statistics
Replies
1
Views
938
  • Set Theory, Logic, Probability, Statistics
Replies
9
Views
1K
  • Set Theory, Logic, Probability, Statistics
Replies
1
Views
991
  • Set Theory, Logic, Probability, Statistics
Replies
15
Views
1K
  • Set Theory, Logic, Probability, Statistics
Replies
4
Views
1K
  • Set Theory, Logic, Probability, Statistics
Replies
1
Views
774
  • Set Theory, Logic, Probability, Statistics
Replies
11
Views
388
  • Set Theory, Logic, Probability, Statistics
Replies
2
Views
3K
  • Set Theory, Logic, Probability, Statistics
Replies
0
Views
989
Back
Top