8assignment - ECEN 303 Assignment 8 Problems 1 If X is a...

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ECEN 303: Assignment 8 Problems: 1. If X is a random variable that is uniformly distributed between - 1 and 1, fnd the PDF of radicalbig | X | and the PDF of - ln | X | . 2. Find the PDF of e X in terms of the PDF of X . Specialize the answer to the case where X is uniformly distributed between 0 and 1. 3. Find the PDF of | X | 1 / 3 and | X | 1 / 4 in terms of the PDF of X . 4. Let X and Y be independent random variables, uniformly distributed in the interval [0 , 1]. Find the CDF and the PDF of | X - Y | . 5. Let X and Y be the Cartesian coordinates of a randomly chosen point (according to a uniform PDF) in the triangle with vertices at (0 , 1), (0 , - 1), and (1 , 0). Find the CDF and the PDF of | X - Y | . 6. Competing exponentials. The lifetimes of two lightbulbs are modeled as independent and exponential variables X and Y , with parameters λ and μ , respectively. The time at which a lightbulb first burns out is Z = min { X,Y } . Show that Z is an exponental random variable with parameter λ + μ .
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