Random Variable:

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Random Variable Variable whose value is a
numerical outcome of a random phenomenon
Example apples X the weight in grams of an
apple
x could be N .
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Random Variables

• Discrete

• Continuous

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• Discrete Random Variable .X
• X has a countable number of outcomes
• the weights of our apples were not finite
• ? The number of classes passed in a year ?
• ? The number of states with snowfall ?
• ? The number of rides taken at the fair ?

4
Discrete Random Variable .X
Each outcome is represented by xi The probability
of each outcome by pi

• 0 pi 1
• Spi 1

5
Continuous Random Variable . Takes on all values
in an interval .with a probability distribution
that is represented by a density curve
Our favorite continuous random variable is ..
NORMAL !!!
Ex time to take a test
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Discrete Random Variable .X
Mean Sxipi Variance S(xi - µ)2pi
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Number of Speeding Tickets
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Rules

• µabX a bµx
• µXY µX µY

Assuming the variables are independent
9
At the Carnival .

• X is the number of times I will ride the
  rollercoaster

• Y is the number of hotdogs that I will eat

• If rides cost 3 and hotdogs are 2 ..
• C to be the cost of my trip to the carnival

10
Go to the farm

• The yield of corn is N ( 120 bushels,20)
• The yield of soybeans is N(85,7)
• Corn makes 15 a bushel and soybeans bring in 23
  a bushel.

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Questions

• What is the mean number of bushels of corn and
  soybeans that I should expect?
• What expected price should I get for them?
• What is the chance that I will farm more than
  215 total bushels?
• What is the chance that I will make more money
  from the soybeans than the corn?

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Test scores
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When is ?

• x x x ? 3x

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Hmm.

• gt A box contains ten 1 bills, five 2 bills,
  three 5 bills, one 10 bill and one 100 bill. A
  person is charged 20 to select one bill.
• gt a) Identify the RV
• gt b) Construct a probability distribution
• gt c) Find the expected value
• gt d) Is the game fair? Explain.

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• Law of Large Numbers
• the average results of many independent
  observations are stable and predictable
• how large is large ?