**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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