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Chapter 7 discrete and random variables

Chapter 7 discrete and random variables. Random variable- variable whose value is a numbered outcome of a random phenomenon ex: let x= #of heads in 4 flips of a coin outcome: tthh x=2. General rules for probability . 1. The p(a) of any event satisfies 0<=p(a)>=1. 2. Sample space must=1

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Chapter 7 discrete and random variables

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  1. Chapter 7 discrete and random variables • Random variable- variable whose value is a numbered outcome of a random phenomenon • ex: let x= #of heads in 4 flips of a coin outcome: tthh x=2

  2. General rules for probability • 1. The p(a) of any event satisfies 0<=p(a)>=1. • 2. Sample space must=1 • 3.the complement = 1-p(a) • 4. 2 events are disjoint if they have no outcomes in common

  3. Probability histogram • The p histogram can be helpful in picturing aDRV • ex: grade :0,1,2,3,4 probability:10%,15%,30%,30%,15%

  4. CRV AND PROBABILITY • continuous random variable-takes all values in an interval of numbers • probability distribution of (x) is described by a density curve • if distribution is normal then the formula z=x-u/stan.dev,is used

  5. CRV APPLICATIONS • When looking for p of an event such as when p(.3<=x=<.7) simply count the units between the outcomes ex:.4

  6. Means and variances • Common symbol for mean of a p distribution is greek letter mu (u) • mean of any discrete variable is a weighted average in which each outcome is by its probability • to find the mean of(x) mult. Each value with its probability and sum

  7. Law of large numbers • As number of observations increase the sample mean will approach the pop. Mean • variance- average of the squared deviations of the variable (x) from the mean (standard deviation is square root of V)

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