Monte Carlo simulations involve the creation of a computer-based model into which variabilities and interrelationships between random variables are entered. A spread of results is obtained when the model is run hundreds or thousands of times. This explains why this…

A student’s t-distribution is a bell-shaped probability distribution symmetrical about its mean. It is regarded as the most suitable distribution to use in the construction of confidence intervals in the following instances:

Continuous compounding applies either when the frequency with at we calculate interest is infinitely large or the time interval is infinitely small. Put quite simply, under continuous compounding, time is viewed as continuous. This is a departure from discrete compounding,…

Using the standard normal distribution table, we can confirm that a normally distributed random variable \(Z\), with a mean equal to 0 and variance equal to 1, is less than or equal to \(z\), i.e., \(P(Z ≤ z)\). However, the…

The standard normal distribution refers to a normal distribution that has been standardized such that it has a mean of 0 and a standard deviation of 1. The shorthand notation used is: $$ N \sim (0, 1) $$ In the…

A confidence interval (CI) gives an “interval estimate” of an unknown population parameter, such as the mean. It gives us the probability that the parameter lies within the stated interval (range). The precision or accuracy of the estimate depends on…

Univariate and multivariate normal distributions are very robust and useful in most statistical procedures. Understanding their form and function will help you learn a lot about most statistical routines.

A random variable is said to have a normal distribution (Gaussian curve) if its values make a smooth curve that assumes a “bell shape.” A normal variable has a mean \(μ\), pronounced as “mu,” and a standard deviation \(σ\), pronounced…

Probability distributions have different shapes and characteristics. As such, we describe a random variable based on the shape of the underlying distribution. A Bernoulli Random Variable A Bernoulli trial is an experiment that has only two outcomes: success (S) or…

The continuous uniform distribution is such that the random variable \(X\) takes values between \(a\) (lower limit) and \(b\) (upper limit). In the field of statistics, \(a\) and \(b\) are known as the parameters of continuous uniform distribution. We cannot…