Chapter%207%20discrete%20and%20random%20variables

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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 x2

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General rules for probability

• 1. The p(a) of any event satisfies 0ltp(a)gt1.
• 2. Sample space must1
• 3.the complement 1-p(a)
• 4. 2 events are disjoint if they have no
  outcomes in common

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Probability histogram

• The p histogram can be helpful in picturing aDRV
• ex grade 0,1,2,3,4 probability10,15,30,30,
  15

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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
  zx-u/stan.dev,is used

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CRV APPLICATIONS

• When looking for p of an event such as when
  p(.3ltxlt.7) simply count the units between the
  outcomes ex.4

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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

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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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