00:01
In this problem, for each of the given binomial distributions, we have to compute the expected value which is the mean, the variance, and the standard deviation.
00:10
So recall that if we have a binomial distribution with the parameters n and p, then the mean is given by n times p, the variance is given by n times p times 1 minus p, and the standard deviation is given as the square root of the variance.
00:26
So first of all, x has a binomial distribution with n is 20 trials, and the probability of success p is 0 .6.
00:36
So the mean is n times p.
00:38
That will be 20 times 0 .6.
00:41
This is 12.
00:42
And the variance will be n times p times 1 minus p.
00:49
So this is going to be 4 .8.
00:51
And the standard deviation is the square root of the variance, the square root of 4 .8, that's approximately 2 .1.
00:58
Now let's move on to the next one.
01:01
N is 15, p is 0 .5.
01:03
So the mean is n times p that is 7 .5...