Defining Probabilities Random Variables - Mercer …：定义的概率随机变量Mercer….pptVIP

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 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 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 Example 3.3, pg 66 P(X = 0) = _____________________ Discrete Probability Distributions The discrete probability distribution function (pdf) f(x) = P(X = x) ≥ 0 Σx f(x) = 1 The cumulative distribution, F(x) F(x) = P(X ≤ x) = Σt ≤ x f(t) 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 The probability histogram 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 Examples: The probabil