I'm working out a proof but I am stuck on something. I'm trying to show that if you estimate probability of success (p) in binomial by x/n, then limit of that estimate with n going to infinity is the true p. I found a source online that shows x/n is a consistent estimator, but I'm getting thrown off by the difference between weak vs strong consistency. I can't find a source that confirms if x/n is weak or strong, and I don't know how you would prove one of the other.
Does it matter whether x/n is weakly or strongly consistent, if I'm trying to show that its limit is p? The definition of weakly consistent looks like it still gets infinitely close, but the probability of convergence is less than 1?