Session-03
What a Random Variable Actually Is (Most Courses Get This Wrong)
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The Interview Puzzle: Creating a Fair Coin from a Biased One
Flip two fair coins: $\Omega = \{HH, HT, TH, TT\}$. One random variable $X$ assigns arbitrary labels $\{0,1,2,3\}$ to the four outcomes. Another random variable $Y$ counts heads, taking values $\{0,1,2\}$. Both live on the same sample space. Why might you prefer $Y$ for most practical questions, and what does the PMF of $Y$ look like?
The PMF of $Y$ is $P(Y=0)=1/4$, $P(Y=1)=1/2$, $P(Y=2)=1/4$. Multiple random variables can coexist on one experiment, each capturing a different aspect. Next we see a richer PMF emerge from the sum of two dice.
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