Respuesta :
Answer:
a) P=0.535
b) P=0.204
c) P=0.286
Step-by-step explanation:
The exponential distribution is expressed as
[tex]F(x>t)=e^{-\lambda t}[/tex]
In this example, λ=1/8=0.125 min⁻¹.
a) The probability of having to wait more than 5 minutes
[tex]F(x>5)=e^{-0.125*5}=e^{-0.625}=0.535[/tex]
b) The probability of having to wait between 10 and 20 minutes
[tex]F(10<x<20)=F(x>10)-F(x>20)=e^{-0.125*10}-e^{-0.125*20}\\\\F(10<x<20)=0.286-0.082=0.204[/tex]
c) The exponential distribution is memory-less, so it is independent of past events.
If you have waited 5 minutes, the probability of waiting more than 15 minutes in total is the same as the probability of waiting 15-5=10 minutes.
[tex]F(x>15|t^*=5)=F(x>15)/F(x>5)=\frac{e^{-0.125*15}}{e^{-0.125*5}}=e^{-0.125*(15-5)}\\\\ F(x>15|t^*=5)=e^{-0.125*(10)}=F(x>10)=0.286[/tex]
