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Distributionshard
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Let X1,X2,X3X_1, X_2, X_3X1​,X2​,X3​ be independent random variables following an Exponential distribution with rate λ\lambdaλ. Define Y=min⁡(X1,X2,X3)Y = \min(X_1, X_2, X_3)Y=min(X1​,X2​,X3​). What is the distribution of YYY?