Foundations for Machine Learning

Currently Playing: Foundations for Machine Learning | Probability Distributions [Lecture 14]

What is the Probability of Exactly 3 Customers Arriving in One Hour if an Average of 5 Customers Visit Your Store per Hour? This question highlights the practical application of the Poisson distribution, a key concept in probability and statistics used to model the likelihood of events occurring within a fixed interval. In this scenario: The average rate is 5 customers per hour. We are calculating the probability of exactly 3 customers arriving in one hour. The formula for the Poisson distribution is: Probability = (λ^k * e^(-λ)) / k! Where: λ is the average number of events (in this case, 5 customers per hour). k is the exact number of events we are interested in (3 customers). Plugging in the values: λ = 5 k = 3 The probability calculation becomes: Probability = (5^3 * e^(-5)) / 3! After solving, the probability is approximately 0.14, or 14%. This practical example shows how distributions help us model real-world scenarios and make informed decisions. Whether in customer behavior, inventory planning, or machine learning, these mathematical tools play a vital role in understanding and predicting outcomes. In this lecture I talk about discrete and continuous probability distributions.