Statistics 270 - Lecture 19

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Statistics 270 - Lecture 19
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• Continue Chapter 5 today

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Definition

• The marginal probability density function for
  continuous random variables X and Y, denoted by
  fX(x) and fY(y), respectively, are given by

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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
• Find the marginal distribution of X

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More Generally
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Independence

• Two random variables X and Y are said to be
  independent if
• Discrete
• Continuous

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Example

• Consider 3 continuous random variables X,Y, and Z
  with joint pdf
• X, Y and Z independent?

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Conditional Probability

• Let X and Y be rvs with joint pdf f(x,y) and
  marginal distribution of X, f(x). The the
  conditional probability density of Y, given Xx
  is defined as
• Substitute the pmfs if X and Y are discrete

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Example

• Consider 2 continuous random variables X, and Y
  with joint pdf
• Find the marginal distribution of X
• Find the conditional distribution of Y given
  X0.2