What is the maximum probability value that a cumulative density function (cdf) can have?
what is the maximum probability any event can have?
i assume it's infinite?
Then you need to review exactly what a "probability" is!
an event which represented by a real number in the range from 0 to 1... however does it apply to all applications?
First of all that is not the definition of probability: probability is not an "event"- although I am sure the definition refers to events. I've never heard of a definition that did not "apply to all applications".
And, to satisfy my curiosity, what does this have to do with differential equations?
for your latter question... i mistakenly posted in the wrong forum... i am new and i don't know how to delete this post and repost it in the probalbility section.
as for my initial question, i am still unclear because of the many different definitions from people and websites. i just want to make sure.
Think about it this way: you can either be guaranteed that an event will take place or you can be less sure until you are guaranteed the event won't take place.
Quantify the above.
The standard definition of "probability" requires that "P(n)= probability that even n happens" be a number from 0 to 1. Thus the largest and probability can be is 1.
Sometimes probability is expressed as a percentage: 0 to 100% is, of course, 0 to 1.
Sometimes you will see "odds" as in "50 to 1 odds against" but that is not "probability". If the odds an event will happen are "a to b against" then the probability that it will happen is b/(a+b) which is always between 0 and 1.
Separate names with a comma.