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Suppose a box contains 10 balls numbered 1,2,3,...10. A random sample of 7 balls is selected. Let X denote the smallest of the numbers drawn. Compute a)Expectation of $X$, $E(X)$. b) Variance of X, Var(X)

I found X's range is $\{1,2,3,4\}$ we need to find the probabilities of getting each of these values, I've got up to this part but I'm confused while I was computing P(X=3), am I supposed to spare the ball numbered as 1,2,3, choose the ball marked 3, like 1/3 and select 6 balls out of balls numbered as 4,5,6,7,8,9,10 (in this case the balled marked as 3 will be the smallest.) like 7 choose 6? so is P(X=3)=[(7 choose 6)* 1/3]/(10 choose 7) correct?

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$$P(X=1)=\frac{9\choose 6}{10\choose 7}$$ $$P(X=2)=\frac{8\choose 6}{10\choose 7}$$ $$\vdots$$ $$P(X=4)=\frac{1}{10\choose 7}$$ and what follows for $$E(X)$$ and $$Var(X)$$?

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