00:01
Once again, welcome to a new problem.
00:04
This time, we're dealing with probability.
00:08
We're dealing with probability theory.
00:11
And when it comes to probability theory, we could think about the expected value.
00:18
We can think about the expected value, and the expected value for probability theory is also the average.
00:28
If i have a probability distribution, if i have a probability distribution, the average tends to be the sum of the expected value or the average is the sum of x times p of x, where p of x is the probability, and of course the x is the variable of interest.
00:59
So we have x and p of x as the variable of interest.
01:04
We also have the standard deviation.
01:08
We have the standard deviation of this type of distribution and that standard deviation comes from the variance.
01:18
Of course, the variance is going to be the expected value of x squared, which is the same as sum of x squared px.
01:26
And if i wanted to find the standard deviation, i would say that the standard deviation for this one is the square root of the expected value of the variance, which is the square root of the sum of x squared p of x.
01:44
Or i could say the standard deviation has its own special formula, which is the same as, which becomes the same as a radical x squared minus x.
01:59
Value of x and then we square that resolved.
02:03
Coming back to this particular problem, we do have specific requirements.
02:10
We have an academician, we have an academician who lives in denizil or denzil or denizli and they work in aiding, adnan, adenian, and they work in aidenon, mandaris university, so they walk over there and they travel, they travel between these two locations by car complaining, complaining about red lights.
03:07
So they do complain about the red lights.
03:10
And these red lights are on nozili district.
03:18
And there's a joint probability distribution, there's a joint probability distribution.
03:28
So when we look at the joint probability distribution, representing data and the type of data that we're looking at is the number of red lights on the road for departure and return trips.
03:51
So we're looking at the number of red lights for departure and return trips.
03:58
X represents the number of red lights and these are red lights on the nazili road.
04:09
And this is based on the departure route so it's based on the departure route from benazli to aiden and then why shows the number of red lights number of red lights on nazli and this is based on the return route in the opposite direction from aiden to denesley.
04:52
So we're going to have the numbers in the table.
04:55
We have a joint probability distribution that we're running.
04:59
And these are your specific numbers that you see in the problem.
05:05
We have the y variable and the y variable has its own component, and 0, 1, 2, 3, and 4.
05:13
And of course, we have the other variable, which is the x variable.
05:18
And we also have the same probability values.
05:23
And within the y and the x variable, we have inputs of interest.
05:32
We have inputs of interest that you're looking at.
05:37
We have inputs of interest that you're looking at.
05:44
So if you look at this problem, if you look at this particular problem, and i'm going to fill in the numbers for the probabilities.
05:59
It's a joint probability distribution.
06:02
So 0 .01 and 0 .03 and 0 .03 and 0 .03 and 0 .02 and 0 .01 .0 .01.
06:11
0 .01, 0 .05, 0 .11, 0 .07, 0 .06, 0 .03, a plus 1 over 100 .23, minus a plus 1 over 100.
06:33
And then we have .10, we have .03, 0 .07, 0 .03, 0 .01, 0 .01, 0 .02, 0 .01, 02 .01, 001, 01 .01.
06:54
So you're looking at the numbers in part a, determine the average number of red lights on departure.
07:11
So we want to look at the average number of red lights on departure in part e...