00:01
So in this one, we're told that the variance of the random variable x is 25, so the standard deviation is the square root of 25 or 5.
00:14
The variance for the variable y is 1, and the standard deviation is the square root of 1, which is 1.
00:22
So x, or stock number one, is more risky because it has a larger standard deviations.
00:35
B, if we have 500 times the expected value of x, well, that's 500 times 8 .45%, which is 42 .25.
00:51
And the variance of 500 times x is 500 squared times the variance of x or 500 squared times 25.
01:07
So the standard deviation is the square root of 500 squared times 25, which is 500 times 5, 2 ,500, at 50 % each, our expected value would be 0 .5x plus 0 .5 y, which is 0 .5 times the expected value of x plus 0 .5 times the expected value of y, which is 0 .5 times 8 .45 % plus 0 .5 times 3 .2%, which is 5 .8%.
02:04
To 5%.
02:06
And the variance of 0 .5 x plus 0 .5 would be 0 .5 squared times the variance of x plus 0 .5 squared times the variance of y plus 2 times 0 .5 times 0 .5 times the covariance which was negative 3.
02:40
So 0 .5 squared is 0 .25 times 25 plus 0 .25 times 1 plus 2 times 0 .25 times negative 3, which gives us a variance of 5...