Normal Distribution
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…
Bernoulli Random Variables and Binomial Random Variables
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…
Properties of Continuous Uniform Distribution
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…
Discrete Uniform Distribution
A discrete random variable can assume a finite or countable number of values. Put simply, it is possible to list all the outcomes. Remember that a random variable is just a quantity whose future outcomes are not known with certainty….
Calculating Probabilities from Cumulative Distribution Function
A cumulative distribution function, \(F(x)\), gives the probability that the random variable \(X\) is less than or equal to \(x\): $$ P(X ≤ x) $$ By analogy, this concept is very similar to the cumulative relative frequency.
Probability Distribution of Discrete and Continous Random Variables
Probability Distribution The probability distribution of a random variable \(X\) is a graphical presentation of the probabilities associated with the possible outcomes of \(X\). A random variable is any quantity for which more than one value is possible. The price…
Time Value of Money With Different Frequencies of Compounding
Time value of money calculations allow us to establish the future value of a given amount of money. The present value (PV) is the money you have today. On the other hand, the future value (FV) is the accumulated amount…
Calculating Effective Annual Rate Given Stated Annual Interest Rate and Compounding Frequency
The effective annual rate of interest (EAR) refers to the rate of return an investor earns in a year, taking the effects of compounding into account. Remember, compounding is the process by which invested funds grow exponentially due to the…
Interest Rate as the Sum of Real Risk-free Rate and Risk Premiums
Interest is a reward a borrower pays for using an asset, usually capital, belonging to a lender. It is compensation for the loss or value depreciation occasioned by the use of the asset. We could also describe it as the…
Interest Rates as Required Rates of Return, Discount Rates, and Opportunity Costs
The time value of money is a concept that states that cash received today is more valuable than cash received in the future. If a person agrees to receive payment in the future, he foregoes the option of earning interest…
