Maximum Likelihood for the Binomial Distribution, Clearly Explained!!!

Maximum likelihood and the binomial distribution, that's what we'll talk about today. StatQuest Hello, I'm Josh Starmer and welcome to StatQuest. Today, we're going to talk about maximum likelihood for the binomial distribution and it's going to be clearly explained. Note, this StatQuest follows up on the StatQuest maximum likelihood clearly explained as well as the StatQuest

probability versus likelihood. And lastly, this StatQuest assumes you are already familiar with the binomial distribution. If not, check out the StatQuest the binomial distribution and test clearly explained. In the StatQuest on the binomial distribution and test, we use the binomial distribution aka this nasty looking thing to determine if, in general, people like orange Fanta more

than grape Fanta. In the context of this problem, X is the number of people who preferred orange Fanta. In this case, X equals 4. N is the total number of people we asked about whether they preferred orange Fanta or grape Fanta. In this case, N equals 7. And P is the probability somebody would

randomly choose orange Fanta over grape Fanta. In this case, P equals 0.5. Altogether, the left side of the equation reads the probability of X, the number of people who say they prefer orange Fanta, given N, the number of people we asked, and P, the probability of picking orange Fanta. Then we just plug the numbers in and

chugged away at the math. And the probability that four out of seven people would randomly prefer orange Fanta is 0.273. Now, if we want to calculate the likelihood of P = 0.5, then all we need to do is rearrange the left side of the equation. That is to say, we change this to this.