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14 236 If X and Y are independent exponential random variables, show that the conditional distribution of X given X Y = t is the uniform distribution on (0,t) Suppose that f(x,y) denotes the joint probability density function of X,Y and f X and f T denote the probability density functions of X and T = X Y respectively. Title Microsoft Word MICROSOFT OFFICEVLCCurtaâ docx Author jbllo Created Date 12/9/ 704 PM. ∀x∀y(x 6= y → f(x) 6= f(y)) f is strictly increasing ≡ ∀x∀y(x < y → f(x) < f(y) f is onto (surjective) ≡ ∀y∃x(f(x) = y) f is a onetoone correspondence (bijective) ≡ f is onetoone∧f is onto If f is a onetoone correspondence, then f has an inverse function f−1 such that ∀x∀y(f(x) = y ↔ x = f−1(y)) Examples.

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