week 4.docx - Week 4 Poisson random variable o Number of success occurring in an interval o o o o o o Ex Number of customer arrivals to a bank in a 1

week 4.docx - Week 4 Poisson random variable o Number of...

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Week 4 Poisson random variable o Number of success occurring in an interval o Ex. Number of customer arrivals to a bank in a 1 hour period o The successes in each interval can range from zero to infinity, theoretically speaking o The probability of more than one success in an interval approaches zero as the interval becomes smaller o The expected number of successes must hold constant for a given interval o The expected number of successes is proportional to the size of the interval o Q4.5 Q1 A real estate office sells 1.6 houses on an average weekday What is the probability of selling 10 or more houses in a dAy? 0.0002 0.2019 0.0000 0.9998 Exponential Distribution o Continuous family of distributions o Used to measure the time that elapses between two occurrences of an event (the time between arrivals) o P ( x≥ x 0 ) = e λ x 0 Relationship between Exponential and Poisson Distributions
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Chapter 6 Normal random variable Normal distribution o Most well known and used o Ex. Annual cost of household insurance
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Unformatted text preview: o Many variables in business are normally distributed o Location is determined by mean o Spread is determined by standard deviation o infinite range Standard normal distribution o Infinite family of curves o However, all normal distributions can be converted into a single distribution called the Z distribution o Process yields standardized normal distribution o Z score gives number of standard deviations a value X, is above or below the mean z = x − μ σ o normal table Calculating probabilities based on Normal Distributions o Finding values of z 4.6 Q1 o Consider an investment whose return is normally distributed with a mean of 10% and a standard deviation of 5% o What is the probability 0.0228 0.4772 0.9772 0.500 o P ( x is equal to or less than 0%) o Z = (0-0.1)/(0.05) = -2 o P ( Z equal to or less than -2) is equal to p( Z equal to or greater than 2) Midterm info LONG STATEMENTS BAYES RULE...
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  • Fall '14
  • IgnacioCastillo

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