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# Defining Probabilities: Random Variables - PowerPoint PPT Presentation

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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## PowerPoint Slideshow about ' Defining Probabilities: Random Variables' - quail-warner

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Presentation Transcript

• 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, ___________

• 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:

_____________________________

• 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:

• Example 3.3, pg 66

P(X = 0) =

_____________________

• 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)

• 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) = ________________

• The probability histogram

• 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.

• 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, __________

• 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.)