Question

10. The times between train arrivals at a certain train station is exponentially distributed with a mean of 10 minutes. I arrived at the station while Dayer was already waiting for the train. If Dayer had already spent 8 minutes before I arrived, determine the following a. b. c· The average length of time I will wait until the next train arrives The probability that I will wait more than 5 minutes until the next train arrives The probability that I will wait between 3 and 6 minutes until the next train ariveS d. Assume that I came to conduct a study on the inter-arrival times of trains at that station. Let Y be a random variable that denotes the time from the instant that I arrived until the arrival of the 4th train. (i) What type of random variable is Y? (ii) What is the PDF of Y? (iii) What is the expected value of Y? (iv) What is the variance of Y?

Answer 1

I- 0.3433 0.61 p(t) 5min) 2061 0

PCL6) -P3) 1- e trafn and it f in vnfts e. no C 40