Our data are:
0.19
0.78
0.96
1.31
2.78
3.16
4.15
4.67
4.85
6.50
7.35
8.01
8.27
12.06
31.75
32.52
33.91
36.71
72.89
From this data we have n=19
Mean is equal to:
We summarize all the values and divide them by the total number of samples.
In another hand we have that Standard Variation is equal to
For this case we take the value of each of our samples, we subtract the average and we square it to that value. We do this with each of the data and in the end we divide them by the total population of the sample (n) minus 1.
if events X and Y are independent, then for intersection we multiply the probability
P(Y∩X) = P(Y) * P(X)
We know that
Now we replace P(Y) * P(X) for P(Y∩X)
Cancel out P(X)
So
Like that
Now we replace P(X) * P(Y) for P(X∩Y)
Cancel out P(Y)
So
P(Y | X) = P(Y) and P(X | Y) = P(X) are true
