Math for Management Notes
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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, were interested in whats 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:
Lets 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
Lets 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%.