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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 __________

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Defining Probabilities: Random Variables

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  1. 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, ___________

  2. 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: _____________________________

  3. 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:

  4. Another Example • Example 3.3, pg 66 P(X = 0) = _____________________

  5. 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)

  6. 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) = ________________

  7. Another View • The probability histogram

  8. 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.

  9. 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, __________

  10. Homework due dates • Friday, 9/3 pg.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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