00:01
We want to find the mean and standard deviation of binomial distributions.
00:06
So remember a binomial has two parameters, n, the number of trials, and p, the probability of success per trial.
00:14
Each trial is independent and they're what we call bernoulli distributions.
00:22
Bernoulli distributions have two outcomes for x, they can either be 1 or 0, success or failure, and then there's the probability of x being p and 1 minus p.
00:34
Only two outcomes.
00:36
So what we're going to do is make use of a couple of facts.
00:40
The first is that the mean of x plus y is equal to the mean of x plus the mean of y.
00:48
And i can make this a little bit more specific and say okay that means the mean of n x is equal to n mu of x.
00:59
This always applies, they don't even have to be independent.
01:04
So what is the mean of the bernoulli? well the expected value of x, this being the mean, can be found by taking each value of x, multiplying it by its probability, and adding them up.
01:18
So if i did that here i'd get p plus 0, so that's just p.
01:25
So each trial has an expected value of p and we have n trials, making the mean of a binomial mu equal to np.
01:37
I didn't need to derive this, you could just memorize this formula, you'd be fine, but might as well know where it comes from.
01:44
The standard deviation happens in a very similar way.
01:49
So this rule is for the mean, the same applies to the variance.
01:53
Not the standard deviation, but the variance.
01:56
Sigma squared n x is equal to n sigma squared x...