00:01
So here we're talking about random variables, and let's just try to think about what's going on.
00:07
We have a whole lot of information here, right? we know that the expected value of a is equal to 8 .2%.
00:15
We know that the standard deviation of a is equal to 1 .249%.
00:21
We know that the expected value of b, a different stock, is...
00:30
Going to be 4 .975 % and the standard deviation of b is going to be 0 .46%.
00:40
Now if we try to think about those probabilities we have a 15 % probability.
00:46
So probability a and b, right? so with a 15 % probability, a is going to be plus 6%.
00:55
And with a 60 % probability, a is going to be plus 8%.
01:00
And with a 25 % probability, they're going to be up 10%.
01:06
B, with the same probabilities are plus 4%, plus 5 % and plus 5 .5%.
01:18
So the first thing we need here is the covariance.
01:22
The covariance is simply the sum of the probabilities, right? the probabilities when we're thinking about how far x or in this case a is from its mean and how far b is, b .j, from its mean, right? so the idea here is we're saying, look, let's wait by the probabilities.
01:49
Let's see if a is above its expected value and if b is above its expected value, right? if they're both above their expected values, we're multiplying positives together and they're moving in a positive direction and otherwise we're getting a negative one, right? so the covariance here be 0 .15.
02:06
The first outcome would be 0 .06 minus 0 .082, right? and then for b, we are going to have 0 .04 minus 0 .475.
02:26
You can see how this is going to get a little messy, plus 0 .0 .04 minus 0 .475.
02:30
Now for the 60 % probability outcome we're thinking about 0 .08 minus 0 .082.
02:40
You see we're comparing to the mean.
02:43
And again for b we have 0 .05 minus 0 .4975.
02:51
Again comparing to the mean...
