A random variable X has pdf fx (x) = e¬* for x 20. Use Chebyshev's inequality to show that P 1X – 11 > 2 < I/4 and show also that the actual probability is e-.

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Q: Find the mean of the random variable X with PDF S 3x² _if 0 <x < 1, f(x) = otherwise.

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Q: 1. Let the random variable X be the time in seconds between incoming telephone calls at a busy…

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Q: 2. Suppose that a continuous random variable X has PDF f(x) = }7 (1 – x²) -1<x<1 else

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Q: Develop a random variate generator for a random variable X with the pdf if x < 0, f(x) = %3D e-2x if…

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Q: Let X1,..., be a sequence of random variables with 1 P(X, = +) = 1 P(X, = 0) = 1 - n2 %3D 2n2 (a)…

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Q: A continuous random variable has a p.d.f. ſkx³(1 – x)²0 < x < 1 | f(x) = Ootherwise

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Q: Consider a random variable X with E[X] = 10, and X being positive. Estimate E[ln√X] using Jensen’s…

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Q: Let X be a random variable with range [0 , 1] and probability density function (pdf) is given as:…

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Q: Let Y be a discrete random variable.  Let c be a constant.   PROVE  Var (Y) = E (Y2) - E (Y)2

A: We have to deduce the formula of variance.