Help verifying a CDF is actually a CDF

[haml]

Hello All,

First post here so thank you for reading and hopefully helping out! I'm feeling stumped with this first question and was hoping someone could help point me in the right direction. I understand, at least I think I do, how to to find the actual probabilities for part b) i, ii and iii but i don't really understand what it means to verify that the CDF there is actually a CDF in part a) .... I attached a picture of the question if it can't be seen let me know and I will type it up.

Thanks any and all.

 

[Dason]

What properties must a CDF meet? http://en.wikipedia.org/wiki/Cumulative_distribution_function#Properties

 

[haml]

ok yeah I guess I knew that I was just thinking I had to integrate it or something..... so with the probability that the shower last over 3 minutes that would be the:

P(x>=3) = Sum going from 3 -> infinity of (1-.4e^(-x/3) - .6(1+(x/5))e^(-x/5))

right?