A log states that beginning at 5:00 pm the time in hours until the first train arrives has an exponential distribution with paramter λ=5.4?
Determnine the probability the first train that arrives after 5 arrives between 5:15 and 5:30
Determine the probability that the first train arrives after 5:30 given that no train has arrived by 5:10
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a/
P(x < t ) = 1 - e^(-λt) = 1 - e^(-5.4t)
t1 = 1/4, t2 = 1/2
P(t1<x<t2) = [(1-e^(-5.4*0.5)] - [1- e^(5.4*0.25)] = 0.1920 <-------
b/
Since the exponential distribution is memoryless,
P(x>1/2) = e^(-λt) = e^(-5.4*0.5) = 0.0672 <-----