00:01
Here we have the probability distribution for the number of computers that are defective in a batch of 4.
00:08
So let's, for simplicity, let's just call this random variable x.
00:11
So here's different values that x can be and their respective probabilities.
00:17
And for part a we're asked to find the mean of the probability distribution.
00:21
So this would be the mean or expected number of computers that are defective in the batch of 4.
00:28
For any discrete random variable, the mean is given by this formula.
00:33
It's the summation over all possible values of the random variable of x times the probability of x.
00:45
So for this distribution, this would be 0 .4096 plus 1 times 0 .4096 plus 2 times 0 .1536 plus 2 times 0 .156, plus 4 times 0 .0016.
01:12
And this comes out to 0 .8.
01:22
And then for part b, we want to find the standard deviation of the distribution.
01:29
So let's first find the variance, and then from that we can just take the square root, which would give us the standard deviation.
01:36
The variance is given by this formula.
01:48
This formula sometimes expressed this way, this latter case being a little bit easier to solve computationally when you're solving manually.
02:04
And so for this distribution, i'm going to skip this.
02:07
The first term because it's 0 times the number, so it's just 0.
02:12
So the second term would be 1 squared times .4096...