Find the pdf of the minimum of 2 independent uniform(0,1) random variables? This is the new concept for me, I was trying to solve it but I'm not exactly sure how to start. Very kind of a suggestion would be helpful.
2026-04-01 03:07:00.1775012820
Suppose that $X_1$ and $X_2$ are continuous random variables with joint cdf $F(x_1,x_2)$ and marginal cdfs $F_1 (x_1)$ and $F_2 (x_2)$ respectively.
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$F(x)=P(min(X_1,X_2)\le x)=P((X_1\le x) \cup (X_2\le x))=P(X_1\le x)+P(X_2\le x)-P((X_1\le x)\cap (X_2\le x))$
Because $X_1$ and $X_2$ are independent, the last term $=P(X_1\le x)P(X_2\le x)$.
Putting all this together $F(x)=2x-x^2$ for uniform distributions $(0,1)$ The pdf $=2-2x$, for $0\le x\le 1$.