MATH 6350

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MATH 6350
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Distributions

• Discrete
• Binomial counts of events in n trials
• Geometric counts of trials to the 1st event
• Poisson counts of events in a set space or
  time
• Continuous
• Normal
• Exponential
• Gamma

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Examples

• Binomial
• Assume that you have n trials and X counts the
  number of successes in these n trials,
• X is binomial if
• Each trials has two outcomes (success or failure)
• The probability of success is the same for every
  trial
• The trials are independent
• The distribution of X is defined by
• P(Xx) nCxpx(1-p)(n-x), for x 0, 1, 2,,
  n

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Binomial

• The binomial distribution of X is defined by
• P(Xx) nCxpx(1-p)(n-x), for x 0, 1, 2,,
  n
• Mean np
• Variance np(1-p)

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Binomial

• Basketball Free Throws
• Video Ex
• http//www.stat.vt.edu/sundar/java/applets/BinDen
  sityApplet.html
• Pick n p

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When does the normal approximate the normal?

• Use applet
• Rule of thumb
• npgt5 and n(1-p)gt5

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Continuous Distribution
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Continuous Example Normal

• Normal
• Mound shaped, symmetrical
• Mean and standard deviation describe the
  distribution
• Empirical Rule
• Standard Normal (z)
• Normal with mean 0 and st dev 1
• Standard Normal Tables
• Show TI-83 calculator, Minitab

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Normal

• Calculators
• http//www.stat.sc.edu/west/applets/normaldemo.ht
  ml
• Example pick mean, standard deviation, find
  probability

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Distribution of the sample mean

• Distribution of the sampling distribution of the
  sample mean
• http//kitchen.stat.vt.edu/sundar/java/applets/CL
  T.html
• Conclusions for sampling distribution
• If n is large enough
• Shape ____
• Mean ____
• St dev ______

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Finding probabilities for sample means

• Ex consider IQ scores with mean 100 st dev
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• A) find probability that a randomly selected
  person has a score of 110 or higher
• B) find the probability that the average IQ of 36
  randomly selected people is 100 or higher?

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Confidence Intervals

• That with repeated sampling thing
• It works with means
• http//www.ruf.rice.edu/lane/stat_sim/conf_interv
  al/index.html
• Or proportions
• http//kitchen.stat.vt.edu/sundar/java/applets/CI
  .html

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