In your own words, describe the difference between the value o...

Question

In your own words, describe the difference between the value of x in a binomial distribution and in the Poisson distribution.

Accepted Answer

All right, hello, everyone. So, this question is asking, how does the interpretation of the variable X differ between the binomial and Poisson distributions? And here we have 4 different answer choices labeled A through D. So first, it's important to recognize what are both the binomial and Poisson distributions, so that we can compare how you would interpret the variable. Starting off with the binomial distribution. Recall that the binomial distribution by definition, models the total number of successes. In a fixed number. Of independent trials. And specifically, it models the number of successes in a fixed number of independent Bernoulli trials. Which just corresponds to yes or no outcomes or success and failure. In this case, the probability P corresponds to that of success and would be the same for each trial since they're independent from each other. Therefore, the variable x would correspond to the total number of successes. In a fixed number of trials and. So how does this compare now to the Poisson distribution? Now, the Poisson distribution models the number of times an event occurs. In a fixed Interval of time. So it's the number of times an event occurs in a fixed interval of time or space, when the events occur independently, and At a constant Average rate labeled lambda. So in the context of the Poisson distribution, the variable X corresponds to the number of Occurrences. Of the event in the given interval. So an example of a binomial distribution is if you toss a coin 10 times and count the number of times it lands tails. An example of a Poisson distribution is counting the number of emails a person receives in, for example, an hour. Assuming they arrive at an average rate. So from here we've arrived at our final answer. Right, in a binomial distribution, X represents the number of successes in a fixed number of trials with the same probability of success each time. In a Poisson distribution, the variable X represents the number of events occurring in a fixed interval. Given that the event itself occurs at a constant rate, and that events are independent from each other. So, going back to the answer choices, the correct answer here is option C, which states in a binomial distribution X is the number of successes in a fixed number of trials. And in the Poisson distribution, X is the number of events in a fixed interval. And there you have it. So with that being said, thank you so very much for watching and I hope you found this helpful.

��app