Math for Management Notes

Supply and Demand

Measures of Center and Variation

Variance is SD squared

Linear Regression

Probability and Distributions

Suppose an experiment consists of trials, and the probability of success in a given trial is . Let be the random variable that represents the total number of successes in all trials (so, in particular, will take on values from 0 to ). Then the probability that you have exactly successes in trials is

where are known as binomial coefficients, which appear in many places in mathematics.

Suppose a class takes a test, and the results are normally distributed with mean 73 and standard deviation of 15. What is the probability that a random student scored above a 90 or below a 50?

In this question, we're interested in what's going on in the tails of the probability distribution. By the rules of probability distributions, the probability that a student scores above a 90 is one minus the probability the student scores below a 90. Therefore, we should calculate:

Let's say represents the random variable corresponding to the experiment "pick a random student and examine their score." Then recasting in terms of random variables, we want to calculate:

We can convert our -values into -values:

Then our probability is the same as

Central Limit Theorem and Hypothesis Testing

Time Value of Money

Let's summarize the above description of compound interest into a nice formula. If an account is established with dollars at an annual interest rate of (expressed as a decimal between 0 and 1), compounded times per year, then at the end of periods the account will be worth dollars, where

Annuity

Suppose that you purchase a house for $250,000. You make a down payment of $50,000, so you finance the balance, $200,000, over thirty years at an annual interest rate of 6 %. Payments are due monthly, so a total of payments are to be made, at a monthly interest rate of , or .5%.