00:01
So here we have to know something about the binomial distribution, right? the binomial distribution is a series of n of them, yes, no trials that are independent and have probability, probability, p.
00:25
Right so it's like flipping a bunch of coins playing a bunch of lottery tickets something that you're doing over and over and over with a fixed independent probability if something is binomial n p it has a mean of n p which should hopefully make a lot of sense right imagine the probability is one you're guaranteed it so if you do it ten times you'll get ten times one ten if the probability is a half you'd expect to get five out of ten you'd get ten times a half five the standard deviation is a little bit ugly, but it's np 1 minus p.
01:00
This should make a lot of sense because, again, if the binomial is zero or one probability, there's not going to be any variance, no standard deviation whatsoever, right? because you're just going to get one -one -one -one or 0 -0 -000 -0.
01:13
And if you put in one or zero into that standard deviation formula, the noise collapses, right? as you get closest to 50 -50, the noise is maximized because that's the area of most uncertainty.
01:23
So now we just need to plug in all these into our formula.
01:28
I can't prove these.
01:30
Proving these takes forever, and i think it's way beyond what is being expected here.
01:36
So here we have a mean of 5 times 0 .1 equals 0 .5.
01:45
We have a standard deviation of 10 times 0 .1 times 0 .9.
01:53
Which is the square root of 0 .9.
01:58
B, we have a binomial distribution with n equals 0 4 and probability of 0 .4.
02:10
This gives me a mean of 4 times 0 .4 equals 1 .6 and a standard deviation of, sorry, i completely botched the first one.
02:22
This is supposed to be 4.
02:24
I don't know why i put a 10 there...