Question

8. Your friend sends you text messages at an average rate of 3 per mimite; the Poisson distribution is a in the next two minutes? (That is. the second text message more than two minutes after the good model. (a) What is the probability that she sends you no text messages between t-0 and t 2.) (b) What is the probability that she sends (c) What is the probability that first? the fourth text message arrives within 30 seconds of the third?

Answer 1

here time between two text messages follow exponential distribution

a)P(no text message in two minutes) =P(X>2)=e^-$\lambda$x =e^-3*2 =0.0025

b)P(2nd text more than 2 minutes after first)=no text message in two minutes) =P(X>2)=e^-$\lambda$x =e^-3*2 =0.0025

c)P(4th arrive within 30 second(0.5 min) of 3rd)=P(T<0.5)=1-e^-3*0.5 =0.7769