Question

Given an exponential distribution with 2 = 10, what is the probability that the arrival time is a. less than X=0.1? b. greater than X= 0.1? c. between X = 0.1 and X = 0.2? d. less than X = 0.1 or greater than X= 0.2? a. P(Arrival time < 0.1)= (Round to four decimal places as needed.)

Answer 1

X ̴ exp (λ = 1 / 10 = 0.1 )

P ( X < x ) = 1 - e^{(-λ* x)}

Part a)
P ( X < 0.1 ) = = 0.0100

Part b)
P ( X > 0.1 ) = = 0.9900

Part c)
P ( 0.1 < X < 0.2 ) = P ( X < 0.2 ) - P ( X < 0.1 )
P ( X < 0.1 ) = = 0.01
P ( X < 0.2 ) = = 0.0198
P ( 0.1 < X < 0.2 ) = 0.0198 - 0.01
P ( 0.1 < X < 0.2 ) = 0.0099

Part d)

less than x = 0.01 or greater than x = 0.2

P ( 0.1 < X) or P ( X > 0.2 ) = 1 - P ( 0.1 < X < 0.2 ) = 1 - 0.0099 = 0.9901