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$HC O_{3}^{-} + H^{+} \to H_{2} C O_{3} \leftrightarrow C O_{2} + H_{2} O$

Let's start with the mathematical definition. Let $G = (V, E)$ be a graph with a set of nodes (vertices) $V$ , a set of edges $E$ , label $y_{v}$ of node $v$ and a neighbors of node $v$ , $N (v)$ , there are 3 types of homophily ratios:

a coding quiz, first numpy 3 numbers, then plot histgram. in red blue and green color respectively.

Multiple Choice

Question 1 of 1

Look at the slide below. Which concept is Hinton introducing here?

Choose the best answer.

Python Challenge

NumPy & Matplotlib: Generate Numbers and Plot a Histogram

Complete the two-part coding challenge below:

Part 1 – NumPy: Use numpy to generate an array of 3 random numbers (use np.random.rand(3) or similar) and print them.
Part 2 – Histogram: Plot a histogram of those 3 numbers where each bar is colored red, blue, and green respectively. Use matplotlib to display the chart.

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Code

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Reference Solution

Conclusion

Great work completing the NumPy & Matplotlib coding challenge! Here's a summary of what you should take away from this exercise:

🔢 What You Learned

NumPy Random Number Generation: How to use np.random.rand(n) to quickly generate an array of n random floating-point numbers between 0 and 1.
Bar Chart Visualization: How to use plt.bar() to create a bar chart, passing x-positions, heights (values), and a list of colors.
Color Customization: How to assign individual colors (red, blue, green) to each bar using the color parameter in Matplotlib.
Chart Labeling: How to add a title, axis labels, and custom tick labels using plt.title(), plt.xlabel(), plt.ylabel(), and plt.xticks().

⚠️ Key Points to Pay Attention To

Bar chart vs. Histogram: plt.bar() is used for categorical/indexed data, while plt.hist() is used for frequency distribution. In this exercise, we used plt.bar() to display individual values with distinct colors — be careful not to confuse the two.
Array Indexing: NumPy arrays are 0-indexed. When setting x-positions as [0, 1, 2], make sure the number of positions matches the length of your data array.
Color List Length: The color list passed to plt.bar() must match the number of bars. A mismatch will cause an error or unexpected coloring.
Randomness: Since np.random.rand() generates different values each run, your chart will look slightly different every time. Use np.random.seed() if you need reproducible results.
Calling plt.show(): Always call plt.show() at the end to render and display your plot, especially in script-based environments.

Multiple Choice

Question 1 of 2

Listen to the clip. Is it in 3/4 or 4/4 time?

$V$

$G = (V, E)$

🚀 Next Steps

Try generating more numbers (e.g., 10 or 100) and use plt.hist() to see a true frequency histogram.
Explore other NumPy functions like np.random.randn() (normal distribution) or np.linspace() for structured data.
Experiment with Matplotlib styling: try adding grid lines, changing bar width, or using a different color palette.

Multiple Choice

Question 1 of 1

Angel and his family go to a restaurant and spend $45 o n f oo d an d$ 9 on drinks. Angel wants to leave a 20% tip. Which proportion will Angel use to find the amount of the tip?