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…
The Elliott Wave Theory
Elliott wave theory was developed by Ralph Nelson Elliott in late 1930s. His discovery changed the perception about stock market trading, which was thought to be chaotic and disorganized at the time. The theory revealed that trading, in fact, follows…
Methods of Solving Counting Problems
Counting problems involve determining the exact number of ways two or more operations or events can be performed simultaneously. For instance, we might be interested in the number of ways to choose 7 chartered analysts comprising 3 women and 4…
Updating Probability Using Bayes’ Formula
Bayes’ formula is used to calculate an updated or posterior probability given a set of prior probabilities for a given event. It is a theorem named after the Reverend T Bayes and is used widely in Bayesian methods of statistical…
