How Can Binomial Distribution Be Solved Without Using a Computer Program?

In summary, the conversation discusses solving a specific equation without using a computer program. The participants suggest using a closed-form solution, but note that it may only work for certain values of N. They also mention using Stirling's approximation to estimate solutions for larger values of N.
  • #1
swede
1
0
Hi!

Does someone know how to solve this equation (see the link) if all variables are known without P_U (without using a computer program)?

http://www.itl.nist.gov/div898/handbook/prc/section2/gifs/pueq.gif

Can it be done in some easy way? I have read courses in calculus at the university, altough it was several years ago :(

regards
swede
 
Physics news on Phys.org
  • #2
I don't think there is a general closed-form solution. You can easily see that this is a N-th order polynomial in P_U. So there will only be a closed form solution up to N=4. For N=4 (or less) I would recommend simply expanding it and plugging it into the quadratic equation or its equivalent.

-Dale
 
  • #3
When N is large, the sum has a maximum at N = p (use Stirling's approximation to see this) and you can approximate the sum with a gaussian function. This will allow you to find approximate solutions.
 

Related to How Can Binomial Distribution Be Solved Without Using a Computer Program?

1. What is the binomial distribution?

The binomial distribution is a probability distribution that describes the likelihood of obtaining a certain number of successes in a fixed number of independent trials, where the probability of success remains constant for each trial. It is commonly used to model events with only two possible outcomes, such as heads or tails in a coin toss.

2. How do you calculate the binomial distribution?

The binomial distribution can be calculated using the formula P(x) = nCx * p^x * (1-p)^(n-x), where n is the number of trials, x is the number of successes, and p is the probability of success in each trial. nCx represents the number of ways to choose x objects from a set of n objects, and can be calculated using the combination formula nCx = n! / (x! * (n-x)!).

3. What is the difference between binomial distribution and normal distribution?

The main difference between binomial distribution and normal distribution is the type of data they are used to model. Binomial distribution is used for discrete data with only two possible outcomes, while normal distribution is used for continuous data with a wide range of possible values. Additionally, the shape of the curves for these distributions is different, with binomial distribution having a skewed shape and normal distribution having a symmetric bell shape.

4. What is the mean and standard deviation in binomial distribution?

The mean of a binomial distribution is equal to n * p, where n is the number of trials and p is the probability of success in each trial. The standard deviation is equal to the square root of n * p * (1-p). These values can be used to calculate the probability of obtaining a certain number of successes or to create a graph of the distribution.

5. In what real-world scenarios is binomial distribution used?

Binomial distribution is commonly used in various fields such as economics, biology, and psychology to model events with two possible outcomes, such as success or failure, yes or no, or heads or tails. Some examples include predicting the success of a marketing campaign, analyzing the effectiveness of a new drug, or studying the probability of passing a test based on guessing.

Similar threads

Variance of binomial distribution
    • Calculus and Beyond Homework Help
Replies
8
Views
1K
MHB How to Solve a Problem Using Binomial Distribution and Normal Table?
    • General Math
Replies
4
Views
3K
I Variable transformation for a multivariate normal distribution
    • Set Theory, Logic, Probability, Statistics
Replies
1
Views
1K
MHB How can I solve P(X>28.41) using the chi-squared distribution?
    • Set Theory, Logic, Probability, Statistics
Replies
1
Views
1K
Poisson & normal distributions as approximations for the binomial
    • Set Theory, Logic, Probability, Statistics
Replies
4
Views
5K
How can I use R to compute confidence intervals for a Poisson distribution?
    • Calculus and Beyond Homework Help
Replies
1
Views
1K
Can a Computer Program Really Teach You Anything You Want to Learn?
    • New Member Introductions
Replies
2
Views
83
I How Does Money Redistribution Affect Poverty Levels in a Simulated Economy?
    • General Math
Replies
28
Views
2K
Engineering Calculating shear center for a "skewed" I beam
    • Engineering and Comp Sci Homework Help
Replies
1
Views
820
Is Alan Turing given too much credit when it comes to computers?
    • Programming and Computer Science
Replies
29
Views
3K

Hot Threads

Recent Insights

Back
Top