# quiz7 - μ and ﬁnite variance σ 2 State Chebyshev’s...

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Math 310-1 (Fall 2010) Name: Quiz #7 Time: 25 minutes 1. A continuous random variable X taking values in [ - 1 , 2] has a density function given by f X ( x ) = ( Cx 2 for x [ - 1 , 2] 0 otherwise where C is some constant. (a) Compute the constant C . (b) Find the distribution function F X . (c) Compute P (0 < X 1). (d) If Y = 2 X , find the distribution function F Y .

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2. (a) Let X be a random variable with finite expectation
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Unformatted text preview: μ and ﬁnite variance σ 2 . State Chebyshev’s Inequality. (b) Consider a nonnegative random variable Y with expectation μ = 5 and variance σ 2 = 1. Use Chebyshev’s Inequality to compute an upper bound for the probability P ( Y ≥ 8)....
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