# chap06 - Statistics for Business and Economics Chapter 6...

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Chap 6-1 Chapter 6 Continuous Random Variables and Probability Distributions Statistics for Business and Economics

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Chap 6-2 Chapter Goals After completing this chapter, you should be able to: Explain the difference between a discrete and a continuous random variable Describe the characteristics of the uniform and normal distributions Translate normal distribution problems into standardized normal distribution problems Find probabilities using a normal distribution table
Chap 6-3 Chapter Goals After completing this chapter, you should be able to: Evaluate the normality assumption Use the normal approximation to the binomial distribution Recognize when to apply the exponential distribution Explain jointly distributed variables and linear combinations of random variables (continued)

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Chap 6-4 Probability Distributions Continuous Probability Distributions Binomial Poisson Hypergeometric Probability Distributions Discrete Probability Distributions Uniform Normal Exponential Ch. 5 Ch. 6
Chap 6-5 Continuous Probability Distributions A continuous random variable is a variable that can assume any value in an interval thickness of an item time required to complete a task temperature of a solution height, in inches These can potentially take on any value, depending only on the ability to measure accurately.

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Chap 6-6 Cumulative Distribution Function The cumulative distribution function , F(x), for a continuous random variable X expresses the probability that X does not exceed the value of x Let a and b be two possible values of X, with a < b. The probability that X lies between a and b is x) P(X F(x) = F(a) F(b) b) X P(a - = < <
Chap 6-7 Probability Density Function The probability density function , f(x), of random variable X has the following properties: 1. f(x) > 0 for all values of x 2. The area under the probability density function f(x) over all values of the random variable X is equal to 1.0 3. The probability that X lies between two values is the area under the density function graph between the two values 4. The cumulative density function F(x 0 ) is the area under the probability density function f(x) from the minimum x value up to x 0 = 0 m x x 0 f(x)dx ) F(x

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Chap 6-8 Probability as an Area a b x f(x) P a x b ( ) Shaded area under the curve is the probability that X is between a and b P a x b ( ) < < = (Note that the probability of any individual value is zero)
Chap 6-9 The Uniform Distribution Probability Distributions Uniform Normal Exponential Continuous Probability Distributions

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Chap 6-10 The Uniform Distribution The uniform distribution is a probability distribution that has equal probabilities for all possible outcomes of the random variable x min x max x f(x) Total area under the uniform probability density function is 1.0
Chap 6-11 The Continuous Uniform Distribution: otherwise 0 b x a if a b 1 - where f(x) = value of the density function at any x value a = minimum value of x b = maximum value of x The Uniform Distribution (continued) f(x) =

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## This note was uploaded on 03/30/2010 for the course STATISTIC Cq498767 taught by Professor Wade during the Spring '10 term at UCSI.

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chap06 - Statistics for Business and Economics Chapter 6...

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