00:01
All right, and your question you're given this table of probabilities, it's probability distribution for two variables, x and y.
00:10
Okay, so what we're trying to do here first is find the expected value of each of the variables.
00:16
And to do that, we take the outcome of the variable.
00:20
So looking at the x, the first outcome is lose $140, and we multiply that to the probability of losing or of that outcome.
00:32
In this case, 0 .1.
00:34
And then we continue that process adding to each other possible outcome.
00:40
50 is the next one, times 0 .3 for its probability, plus 150 times 0 .4, plus 190 times 0 .2.
00:58
Now i'm going to type that in a calculator, but i'm going to go ahead and get the expected value for y written out as well.
01:05
So that's going to be set up the same way.
01:07
It's just negative 30 first outcome times its probability .1 plus 30 times 0 .3 plus 100 times 0 .4 plus 170 times 0 .2.
01:29
All right, i'm going to go ahead and pause the video now and type that in.
01:32
I'll be right back.
01:33
All right, so you can see what i put down there.
01:36
You were to type an integer answer, and they worked out to 99 for the first one, and 80 for the second one.
01:44
99 for x, 80 for y.
01:48
All right, moving on to the standard deviation.
01:51
What we have to do for standard deviation is take the square root.
01:56
This is going to be rather long here, so i'll just extend that, and we take the mean.
02:02
Now we're working with x, so the mean for x was 99.
02:08
We take each value, negative 140, each possible outcome, minus the mean, then we square it, and we times it to the probability of that outcome, which is 0 .1, and add, and do this for every possible outcome.
02:26
So the next one's going to be 50 minus 99 squared times 0 .2 plus the next outcome is 150 minus 99.
02:42
Squared times 0 .4.
02:46
I just noticed i typed the wrong probability there.
02:50
That should be 0 .3...