I'm currently learning binomial random variable on Khan academy and in one of the video, Sal said that in order for a random variable to qualify as a binomial random variable, it has to meet four conditions
1) the outcome of each trail can be classified as success or failure
2) each trail is independent of each other
3) there is a fixed number of trails
4) the probability of success on each trail is constant
Could someone please explain the logic behind point 3? Why is fixed number of trail a requirement for random variable to qualify as a binomial random variable?
Because he says so. Really. When you get to define a new kind of random variable of your own, you will be able to make the rules.
OK, technically it's not because Sal said so; it's because Sal's definition is consistent with what mathematicians have meant by "binomial random variable" for hundreds of years.
Also, technically, I disagree that Sal's four conditions are really necessary--what is necessary is that you get the same end result as those four conditions produce. You can produce the result any way that works; but I think you'll have a hard time getting the same result if you take condtions 1, 2, 4 and not 3. It might be a useful exercise to try it and see if you can.