The time between arrivals of taxis at a busy intersection is exponentially distributed with a mean of 24 minutes. (a) What is the probability that you wait longer than one hour for a taxi? (b) Suppose you have already been waiting for one hour for a taxi, what is the probability that one arrives within the next 10 minutes? Round your answers to 4 decimal places.

Step-by-step explanation:

Given that:

X ~ Exp (β=24)

What is the probability that you wait longer than one hour for a taxi?

Pdf: f(x) =   , 0 < x

Cdf: P(X ≤ x) =  

P(X  ≤ x) =         for x > 0 ⇒ P ( X > x) =

Thus, the probability that you wait longer than one hour for a taxi = 0.0821

b)

≅ 0.340759

 = 0.3408

The probability that one arrives within the next 10 minutes = 0.3408

maya’s expression will generate the wrong sum because she violated the commutative property.

step-by-step explanation: