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Defining Probabilities: Random Variables

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- 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, ___________

- 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

- 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:
_____________________________

- 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 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, __________

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

- 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.)