Math 135 Week 12 Lecture Notes Bittenger 10th

1 27 suppose a runner from the 2008 olympic mens

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Unformatted text preview: nuous Random Variables Example 3: Athletes competing in the 2008 Olympics men’s marathon finished the race between 2.1 and 2.7 hours. If x is the number of hours a certain runner finished the race, then x is a continuous random variable distributed over the interval [ 2.1, 2.7 ] . Suppose a runner from the 2008 Olympic men’s marathon is selected at random, what is the probability that this runner completed the race in between 2.4 and 2.6 hours? Math 135 Class Notes – Week 12 Bittenger 10th Ed. 3 DEFINITION: Let x be a continuous randon variable. A function f is said to be a probability density function for x if: 1. For all x in the domain of f, we have 0 ≤ f ( x ) . 2. The area under the graph of f is 1. 3. For any subinterval [ c, d ] in the domain of f, the probability that x will be in that subinterval is given by P ([ c, d ]) = ∫ f ( x ) dx . d c Example 4: The time between arrivals of subway trains at a station is modeled by 10 h ( x ) = 2 , for 5 ≤ x ≤ 10 , where x is in minutes. x a. Verify that h is a probability density function. b. Find the probability that the time between trains is bet...
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This document was uploaded on 02/19/2014 for the course MATH 135 at CSU Chico.

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