import pandas as pd

Prepare the table columns

data = { 'X': X, 'P(X)': P_X, 'X * P(X)': [x * p for x, p in zip(X, P_X)], '(X - μ)': [x - mean for x in X], '(X - μ)^2 * P(X)': [(x - mean) ** 2 * p for x, p in zip(X, P_X)] }

Create the DataFrame

df = pd.DataFrame(data) dfHere is the filled table with the calculated values:

X	P(X)	X * P(X)	(X - μ)	(X - μ)² * P(X)
0	0.07	0.00	-2.4	0.4032
1	0.18	0.18	-1.4	0.3528
2	0.38	0.76	-0.4	0.0608
3	0.12	0.36	0.6	0.0432
4	0.15	0.60	1.6	0.3840
5	0.10	0.50	2.6	0.6760

Total for $X \cdot P(X)$ (Mean $\mu$): 2.4
Total for $(X - \mu)^2 \cdot P(X)$ (Variance $\sigma^2$): 1.92

Do you have any other questions?

Here are 5 additional questions you might explore:

1. How does altering the probabilities affect the distribution's mean and variance?
2. Why is variance a good measure of dispersion in a dataset?
3. Can two different distributions have the same mean but different variances?
4. What happens to the standard deviation when all probabilities are the same?
5. How can we visualize this probability distribution using a graph?

Tip: It's useful to create visual representations (such as histograms) to better understand how data is distributed.