Statistics 270 - Lecture 18

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Statistics 270 - Lecture 18
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• Will begin Chapter 5 today

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• Many situations where one is interested in more
  than one random variable
• Have a joint distribution for such cases

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Example

• Let X and Y be random variables with pmf

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Definition

• Let X and Y be rvs on a sample space S
• Discrete rvs The joint prob. mass function for
  each (x,y) is defined by p(x,y)P(Xx, Yy)
• If A is an event then,

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Discrete RVs

• Usual properties of pmfs still hold

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Example

• Let X and Y be random variables with pmf
• Observations
• P(X2,Y2)
• P(Xgt1, Y1)

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Example

• Let X be the number of Canon digital cameras sold
  in a week at a certain store
• The pmf for X is
• 60 of all customers who purchase camera also
  purchase the long-term warranty
• Determine the joint pdf of X and Y

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Definition

• The marginal probability mass function for
  discrete random varaibles X and Y, denote by
  pX(x) and pY(y), respectively, are given by

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Example

• Let X be the number of Canon digital cameras sold
  in a week at a certain store
• The pmf for X is
• 60 of all customers who purchase camera also
  purchase the long-term warranty
• Find the marginal distributions of X and Y

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Definition

• Let X and Y be rvs on a sample space S
• Continuous rvs The joint prob. Distribution
  function for (x,y) is defined by f(x,y)
• If A is an event then,

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Continuous rvs

• Usual properties of pdfs still hold

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Example

• The front tire on a particular type of car is
  suppose to be filled to a pressure of 26 psi
• Suppose the actual air pressure in EACH tire is a
  random variable (X for the right side Y for the
  left side) with joint pdf
• Notice that they seem to vary jointly