Flipping Coins

1
Flipping Coins

• Warm-up Activity
• Six identical coins to be flipped 10 times
• Tally results (for example, HTTHTT 2 Heads)
• Clearly, results range from
• 0 Heads ? 6 Heads or 6 Tails ? 0 Tails
• Construct a Histogram
• Special Consideration
• Exercise 1 Flip and Tally
• Exercise 2 Make up random-looking results

2
Class Acitivity Results
Exercise 1 Make up random-looking results
of Heads
Exercise 2 Flip and Tally
3
Flipping CoinsResults
How many?

• gt sample(01,6,replaceT,probc(0.5,0.5))
• 1 1 1 1 0 1 0
• Ten Times
• NHeadslt-rep(NA,10)
• for(i in 110)
• Resultlt-sample(01,6,replaceT,probc(0.5,0.5))
• NHeadsilt-sum(Result)
• gt NHeads
• 1 4 3 3 3 0 2 3 4 3 3

Possible items (numbers or characters) to choose
from
gt par(labc(6,6,10),lwd2) gt hist(NHeads,breaksse
q(-.5,6.5,by1),col"salmon2") gt box()
4
Probability Distributions

• Random Phenomena
• Histograms are one way to summarize probabilities
• hist(data,prpbabilityT)
• Uncertain outcomes ? Probabilities
• Examples,
• Rain Tomorrow?
• Traffic on the Turnpike
• Number of snowy days
• How do we understand variability?
• Usually compute a Mean, Expected, Average Value
  and some variability around it.
• Probability Density Functions (PDF) provide a
  compact description of random phenomena. Normal
  or Gaussian is extensively used.

Some measure of variability
Probability Density
X
Mean(m)
5
Normal Distribution
This slide full of Math Expressions

• Area under the PDF (integral)
• For Normal Distribution,
• This distribution is spread over the entire
  number line
• A Cumulative Density Function (CDF) computes the
  probability,

To come up with the Normal Distribution for your
data, need m and s
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Normal DistributionCAN R SIMPLIFY MATTERS?

• Accessing and Reading the Temperature data in to
  R
• ?read.table()
• locc(http//www.civil.umaine.edu/ewre/sjain/AnnT
  MidlandTx.txt)
• read.table(loc,skip1)-gtTdata
• For example,
• To read from a file
• read.table(c/Texas/T.txt)
• Look up header nrows options

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Summarizing DataCAN R SIMPLIFY MATTERS?
year

• Temperature data is stored in Tdata
• Tdata,2
• Recall, we need Mean and Standard Deviation to
  define the Normal Distribution for the
  Temperature data

Annual Temp.
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Summarizing DataCAN R SIMPLIFY MATTERS?
Sum of all temperature values, divided by the
number of values
Remove mean from all temperature values, square
them and compute the sum divide by (n-1) and
take square root
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Summarizing Data? Probabilistic Description
10
Normal Distribution Computing Exceedance other
probabilities