probability mass functionDr. Courtney said:
Probability is the study of the likelihood or chance of events occurring, while statistics is the collection, analysis, and interpretation of data to make inferences about a population.
Calculus is used in probability and statistics to determine the probability of continuous events and to calculate the area under a curve, which is often used to represent probability distributions.
The mean is calculated by finding the sum of all the data points and dividing by the total number of data points. The median is the middle value when the data is arranged in ascending or descending order. The mode is the most frequently occurring value in the data set.
The central limit theorem states that the means of a large number of independent samples from a population will be approximately normally distributed, regardless of the shape of the population's distribution. This is important because it allows us to make inferences about a population based on a sample, which is often more feasible and less costly.
Two events are considered independent if the probability of one event occurring does not affect the probability of the other event occurring. This can be determined by calculating the joint probability of the two events and comparing it to the individual probabilities of each event. If the joint probability is equal to the product of the individual probabilities, then the events are independent.