## What four conditions are necessary for x to have a binomial distribution?

The answer to this question is what the title says. The key to understanding what these four conditions are, and what they mean, is knowing what a binomial distribution is. A binomial distribution has two properties: 1) It can be written in terms of probabilities and 2) it assumes that the trials being analyzed are independent from each other (meaning that one trial does not affect another). If you want your data set to have a binomial distribution, then the following conditions must be met: 1) All trials must be independent of each other 2) There must only be two outcomes per trial 3) there must either be no limit on how many trials could take place or the limit must be fixed and certain (ex. if there are 100 trials, what will happen is either x% of people will succeed or y% of people will fail) These properties ensure that your data has a binomial distribution because it shows how probability plays into trial outcomes.

All trials must be independent from each other – There must only be two possible outcomes per trial – The number of events in one group cannot exceed 20 with more than 50 total cases per event type being observed within the study. You can’t have any restrictions on what percentage a success would entail nor what percentage an outcome should end up as failure; this constraint applies to those who want their data set to have a binomial distribution.

### The probability of success is the same for all trials (or what you call ‘success’ and what you call a failure)

Each trial must be independent from each other – this means that knowing what happened to one person, will not affect what happens to another. For example, if I flip a coin twice and it lands on heads both times, my data set would have no binomial distribution because there are two outcomes but they’re related to each other in some way due to the fact that I know what’s happening with the first result before flipping again.

It can’t be determined how many trials will end up as successes or failures; this constraint applies when someone wants their data set to have a binomial distribution, but doesn’t know what the probability of a success is The trials must be individual and not grouped together – if I flip a coin twice so that my data set has four outcomes: two heads and two tails, this would have been better as one trial with four possibilities rather than having to deal with it on an individual basis. This means that different people’s results are accounted for separately;

### Each person flips the coin once, then we get what happens when they do, which is what makes up our data set.

In order to create a dataset whose x values will follow a binomial distribution there are three constraints necessary: firstly, the number of successes in any given group must always equal half or less of the total number of trials. Secondly, each trial must be independent – what happens to one person doesn’t affect what another will do in their turn. Finally, there should only be two possible outcomes – for example flipping a coin (as long as what they get is either heads or tails).

We also want a larger sample size so that our data has more accuracy and less error, which means we need to increase the number of flips per individual’s turn if necessary.”

- The trials must not be grouped together
- Each trial needs to be independent from any other
- There are only two potential outcomes: success or failure

“In order to create a dataset whose x values will follow a binomial distribution there are four conditions that must be met. Firstly, the number of trials needs to be a perfect ratio so it’s possible to count each trial (i.e., there are 20 flips per person). Secondly, each trial must not depend on what happened in any other trial – what happens with one individual doesn’t affect what another will do in their turn. For example flipping coins and making sure they get either heads or tails is okay as long as what they get is either heads or tails.”

- The trials need to happen at random

- There can only be two potential outcomes: success or failure

- We want more accurate data which means we should increase the size of our sample if necessary