Hi PF, i have several questions about univariate statistics that doesnt seem to be covered in my notes or online, i hope the question is not redundant on the forums, but i ran a search and saw nothing. In univariate statistics, you can have a PMF which is a discrete random variable (RV) and a PDF which is a continuous RV. "We can estimate these quantities given a random sample of observations on a random variable, specifically, a random sample of n independently sampled observations on the random variable X is a set of random variable, each of which has the same distribution as X. That is, letting Fx(x) denote the CDF of Xi." we can say that random variables, are independent and identically distributed (IID), since each observation has the same distribution, E(X) and variance are the same thus COV(Xi,Xj) = 0" What happens if it was a PMF or is it not possible? A normal distribution of method of moments tell us: 1st mom = E(X) 2nd mom = Variance 3rd mom = skewness 4th mom = Kurtosis Does the skewness tell us the direction which the curve is skewed and if the E(X) and variance is on the left side or right side of the curve? What is kurtosis and what does it tell us? in my notes i have that the kurtosis tells me that it is a function of the first 4 moments which tells me the E(X), variance, skewness and kurtosis, but doesn't exactly tell me about kurtosis. could i possibly get an explanation?