Byroz223
On his way to work, Mr. Mustermann has to wait for the train every morning and then again for a bus. The waiting times for the train and bus are independent of each other and exponentially distributed with parameters λ1 and λ2, where λ1 is not equal to λ2. Determine the distribution function of the total waiting time and the expected value of the shorter waiting time.
(2 votes)
Loading...Hello, Is the €29 concessionary ticket the discounted version of the €49 ticket? If so, can I use it to travel throughout Germany by bus and train (except ICE)? Kind regards
In Austria, some trains are designated with D in the timetable. What does D mean?
If I could drive, it would be enough if I got up at 6:30 and then I could still shower and have breakfast, and it would be quite relaxed. For example, according to Google maps, I would have to leave at 7:05 at the latest, taking traffic jams into account, in order to reach my…
You must fold the distributions in order to obtain the distribution of the sum, i.e. the total waiting period, for t > 0:
Integral ( 0 to t ) λ1 * exp( -λ1 * (t-s)) * λ2 * exp( -λ2 *s) ds =
λ1 * λ2 * exp( -λ1 * t) * Integral( 0 to t ) exp( -(λ2 -λ1) * s) ds =
…. now you just have to calculate the integral and summarize a bit.
For the expected value of the shorter waiting time, i.e. the minimum from both waiting times, it is necessary to know that this is again exponentially distributed (with parameter λ1 +λ2).