00:01
So here we have a probability density function or a probability distribution function for a discrete variable x.
00:14
And the sum of all of these must equal 1.
00:21
So it meets a 0 .14 plus 3a plus 0 .24 plus 0 .17.
00:30
Is 1.
00:31
That means that 3a is 1 minus.
00:35
Let's see here.
00:37
0 .14 plus 0 .24 plus 0 .17, 0 .55.
00:46
So this is 0 .45.
00:49
And it means then that a is 0 .45 divided by 3 is 0 .15.
00:57
So this then is 0 .45 .5.
00:58
So this then is 0 .45.
01:00
0 .15.
01:04
Then what is the expected value for x? well, the expected value of x is going to be the sum over o x of x times the probability that x is x.
01:23
So this then is 0 times 0 .14 plus 1 times 0 .3.
01:32
Plus two times 0 .15 plus three times 0 .24 plus 4 times 0 .17.
01:59
It is equal to 2 .00 or just 2 .0.
02:07
The expected value of x squared is going to be to sum over 0x of x squared.
02:15
Times the probability that x is x.
02:18
So that is 0 squared times 0 .14 plus 1 squared times 0 .30 plus 2 squared times 0 .15 plus 3 squared times 0 .24 plus 4 squared times 0 .17.
02:38
And that is equal to, let's see here, 0 .3 plus 3 plus 4 squared times 0 .17 .7.
02:51
Plus 2 squared times .15 plus 3 squared times .25 plus 3 squared times .24 plus 4 squared times .17.
03:17
So this is 5 .78.
03:31
And that means that the variance for x is going to be 5 .7.
03:38
Minus 2 squared, which is 1 .78.
03:45
That means that the standard deviation, x is going to be the square root of 1 .78, which is equal to 1 .3342...