Introduction to Probability: Student's T Distribution

Key Takeaways

hello folks in this lesson we are going to talk about the student's t-distribution and its characteristics before we begin we use the lowercase letter T to define a student's t-distribution followed by a single parameter in parentheses called degrees of freedom we read this next statement as variable Y follows a student's t-distribution with 3 degrees of freedom as we mentioned in the last video it is a small sample size approximation of a normal distribution in instances where we would assume a normal distribution were it not for the limited number of observations we use the student's t-distribution for instance the average lap times for the entire season of a Formula One race follow a normal distribution but the lap times for the first lap of the Monaco Grand Prix would follow a student's t-distribution now the curve of the student's t-distribution is also bell-shaped and symmetric however it has fatter tails to accommodate the occurrence of values far away from the mean that is because if such a value features in our limited data it would be representing a bigger part of the total another key difference between the students T distribution and the normal one is that apart from the mean and variance we must also define the degrees of freedom for the distribution great job as long as we have at least two degrees of freedom the expected value of a T distribution is the mean mu furthermore the variance of the distribution equals the variance of the sample times the number of degrees of freedom over degrees of freedom minus 2 overall the student's t-distribution is frequently used when conducting statistical analysis it plays a major role when we want to do hypothesis testing with limited data since we also have a table summarizing the most important values of its CDF great another distribution that is commonly used in statistical analysis is the chi-squared distribution in the next video we will explore when we use it and what other distributions it is related to thanks for watching if you found this video interesting and want to gain an edge in your career make sure to LIKE comment and subscribe and don't forget to check out some of our other videos for another quick win in the data science skills department