How Many Cups of Coffee Can I Buy with $10?

Sat, 25 Jan 2025 00:00:00 +0000

Imagine this: I’m a coffee lover with only 10 dollars to spend. But here’s the twist—each cup of coffee costs a random price between 0 and 10 dollars. So, on average, how many cups can I actually buy?

If you’re curious about the answer, check out the video!

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Buying Coffee

For a theoretical justification (a little probability theory is needed), you can watch the video (in Chinese) below:

What Is the Sample Space in Statistics?

Wed, 13 Nov 2024 00:00:00 +0000

In statistics, we often work with independently and identically distributed (iid) samples. For instance, consider a set of observations: $ (X_1, X_2,\dots,X_{10}). $ However, what is the underlying sample space (a foundational concept from probability) associated with these samples?

Specifically, let’s take an element $ \omega\in\Omega, $ where this $ \omega $ represent an individual like Alice. How, then, could we use $ X_1 $ to denote Alice and, simultaneously, $ X_2 $ to denote another individual, say Bob?

This question once confused me for years. If you are having the same trouble, check out the video!

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Sample Space

Probability | Zhu Xuelin

How Many Cups of Coffee Can I Buy with $10?

What Is the Sample Space in Statistics?