I have an important presentation on tuesday about the exponential distribuion as a density function. My question is: What are the advantages of using this function?
In order to fulfill my task i have to show that this function is "right" and that i can calculate the probability of a certain event. So i have this task: A bubble pops "in the next second" with the probability of 2%. Calculate the probability for a.) the bubble pops after one second b.) the bubble pops after ten seconds.
I already have the answers to this task. But my problem is, that i thought, that the exponential distribution and the corresponding density function would be so helpful, because i can get the probability for longer time intervals. But i was able to find the correct answers to my task above without using the density function. Then i calculated the probability again with the density function and i have the same solution.
So what are the advantages then?
It would be great, if anyone would have an answer to my question. Oh, and sorry for my English :) Emily
An obvious advantage of using the answer: $$P_{popped}(t)=1-0.98^t$$ Is that you can plug in an arbitrary value for $t$. It doesn't have to be a whole number. You can then do $1-P_{popped}(t)$ to find $P_{survived}(t)$: $$P_{survived}(t)=0.98^t$$ It's also a bit easier I suppose to envision the trend of $P(t)$ when using this function rather than looking at discrete probabilities:
I'm not sure why the dots aren't lined up perfectly with the line here, but you get the point.