The ONLY Hour of Probability Distribution Practice You Will EVER Need

Welcome everyone. We're going to explore some really fundamental probability distributions. First up, problem one, website conversion. Imagine a potential customer visits your e-commerce website. There's a 3% chance they will make a purchase. So, part A asks, which distribution models whether this specific customer completes a purchase? Let's think about the clues here. We're looking at a single customer and there are really only two outcomes, right?

They either buy or they don't. That's right. It's the Berni distribution. It's the simplest one, perfect for a single trial with a binary outcome. We can say X= 1 for a purchase, which happens with a probability P of 0.03, and X= 0 for no purchase with a probability of 1 minus P, which is 0.97.

Simple as that. Okay, so for part B, what is the expected value or the mean for this situation? And what's the probability they don't make a purchase? Here's the great thing about Berni. The formula is super easy. The expected value for a Bernoli distribution is simply P. So in our case, the expected value E of X is 0.03. And the probability of no purchase, well, that's just

1 minus P. So we do 1 - 0.0 03 which gives us 0.97 or 97%. Fantastic. Let's move on to problem two. Customer service calls. A call center receives calls at an average rate of 15 calls per hour. The question for part A is which distribution models the number of calls received in a 15minute period.

The key hints here are that we're counting random events over a fixed time period. Does a specific distribution come to mind? You got it. It's the plus distribution. It's perfect for this. Now, here's the first step, and it's an important one. We have to scale the rate, which we call lambda for our 15-minute period. The original rate is 15 calls per hour. So, we take 15 and multiply it by