Defining probabilities random variables
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Defining Probabilities: Random Variables. Examples: Out of 100 heart catheterization procedures performed at a local hospital each year, the probability that more than five of them will result in complications is __________

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Defining Probabilities: Random Variables

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Defining probabilities random variables

Defining Probabilities: Random Variables

  • Examples:

    • Out of 100 heart catheterization procedures performed at a local hospital each year, the probability that more than five of them will result in complications is

      __________

    • Drywall anchors are sold in packs of 50 at the local hardware store. The probability that no more than 3 will be defective is

      __________

    • In general, ___________


Discrete random variables

Discrete Random Variables

  • Example:

    • Look back at problem 3, page 46. Assume someone spends $75 to buy 3 envelopes. The sample space describing the presence of $10 bills (H) vs bills that are not $10 (N) is:

      _____________________________

    • The random variable associated with this situation, X, reflects the outcome of the choice and can take on the values:

      _____________________________


Discrete probability distributions

Discrete Probability Distributions

  • The probability that there are no $10 in the group is

    P(X = 0) = ___________________

    (recall results from last time)

  • The probability distribution associated with the number of $10 bills is given by:


Another example

Another Example

  • Example 3.3, pg 66

    P(X = 0) =

    _____________________


Discrete probability distributions1

Discrete Probability Distributions

  • The discrete probability distribution function (pdf)

    • f(x) = P(X = x) ≥ 0

    • Σxf(x) = 1

  • The cumulative distribution,F(x)

    • F(x) = P(X ≤ x) = Σt ≤ xf(t)


Probability distributions

Probability Distributions

  • From our example, the probability that no more than 2 of the envelopes contain $10 bills is

    P(X ≤ 2) = F(2) = _________________

  • The probability that no fewer than 2 envelopes contain $10 bills is

    P(X ≥ 2) = 1 - P(X ≤ 1) = 1 - F(1) = ________________


Another view

Another View

  • The probability histogram


Your turn

Your Turn …

  • The output from of the same type of circuit board from two assembly lines is mixed into one storage tray. In a tray of 10 circuit boards, 6 are from line A and 4 from line B. If the inspector chooses 2 boards from the tray, show the probability distribution function associated with the selected boards being from line A.


Continuous probability distributions

Continuous Probability Distributions

  • Examples:

    • The probability that the average daily temperature in Georgia during the month of August falls between 90 and 95 degrees is

      __________

    • The probability that a given part will fail before 1000 hours of use is

      __________

    • In general, __________


Homework due dates

Homework due dates

  • Friday, 9/3pg.54-56

  • Wednesday, 9/8 pg. 72-74 (both sets)

    (Check the web site on Thursday, 9/2, for an updated schedule.)


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