Question

Please review and explain the significance of basic concepts about random variables, namely, the mean, the variance, the standard deviation, and the correlation. Provide your explanations and definitions in detail and be precise. Comment on your findings. Provide references for content when necessary. please give a detailed answer. thank you

Answer 1

A random variable is a variable whose value is unknown or a function that assigns values to each of an experiment's outcomes. - standard deviation is a statistic that looks at how far from the mean a group of number is, by using the square root of variance. The calculation of variance uses squares because it weighs outliers more heavily than data closer to mean. This calculation also prevents difference above the mean from cancelling out those below which would result in variance of zero. The standard deviation is the square root of variance. =√Var (X)

variance- The variance is the average of the squared differences from mean. To figure out the variance, first calculate the difference between each point and the mean; then, square and average the result. Var(X)= Standard deviation and variance both are determined by using mean of a group of numbers in question. These are basic mathematical concepts that play important role throughout the financial sector, including the areas of accounting, economics and investing. - Mean- The most important characteristic of any probability distribution are the mean ( or average value). The mean of a discrete random variable X is a weighted average of the possible values that the random variable can take. Unlike the sample mean of a group of observations, which gives each observation equal weight, the mean of random variable weights each outcome xi according to its probability,pi. The common symbol for mean is formally defined by.   = =