00:01
All right, so we're going to try to determine the cumulative distribution function, the cdf, of the binomial random variable.
00:10
So that's going to be bin, sample of three, and a probability of 25%.
00:21
So that means we'll have just a couple of probabilities to calculate here.
00:27
This is going to mean that our probability mass function, which we're going to get from the binomial, is going to be the f of x our pmf of three choose x and then we get our probability of 0 .25 raised to the power of x and the probability of 1 minus 0 .25 or 0 .75 raise the power of 3 minus x so that's what our probability is going to be and this is going to be for x equals 1.
01:14
Wait, actually we're going to be doing 0 as well, so 0, 1, 2, and 3.
01:24
So that's going to look like this.
01:32
It's going to be 0 for everything less than 0, because that's how we start off.
01:38
And then for the ones between 0 and 1, that is going to be, if we choose exactly 0, that's going to be the f of 0, which is going to equal 3 choose 0, which is just going to be 1 times 0 .25 to the power of 0, which is just going to be 1.
02:02
And then we'll have 0 .75 cubed, and that's going to equal 42, 1875.
02:18
And then we'll add that on to the next probability.
02:22
That's going to be between 0 and 1, including 0, excluding 1, excluding 1...