### How to use EXCEL as a probability density distribution graph

Specific steps are as follows:

1, first of all, open the need to operate the excel table, as shown in the figure below, and then go to the next step.

2, second, select all the data, click on the scatterplot, select the first style, as shown in the figure below, and then go to the next step.

3. Next, you can see the initial scatterplot, as shown below, and then go to the next step.

4, then, select the Y-axis, right-click the mouse, and then select the “Add Secondary Grid Lines” option, as shown below, and then go to the next step.

5, then, you can see in the Y-axis to add a secondary grid lines, as shown below, and then go to the next step.

6, finally, the same, you can add a grid line on the X axis. You can see the effect image, as shown below. Thus, the problem is solved.

### How to draw the probability density function p(x,y)=4xy

How to draw the probability density function p(xy)=4xy: calculate fx, fy, if fx*fy=f(x,y) is independent, fx=2X, fy=2y.

P=∫(0–>1) e^(-y)dy∫(0–>1-y)2e^(-2x)dx.

=∫(0–>1)e^(-y)(1-e^(2(1-y))dy.

=∫ (0–>1)(e^(-y)-e^2e^y)dy.

=(1-e)(1+e^2).

Implications

There is no practical significance in speaking of probability density alone; it must be predicated on a definite bounded interval. You can think of the probability density as a vertical coordinate, the interval as a horizontal coordinate, the integral of the probability density over the interval is the area, and this area is the probability of the event occurring in this interval, and the sum of all the areas is 1. So analyzing the probability density of a single point alone doesn’t make any sense, and it has to have the interval as a reference and comparison.