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Problem 1: The diameter X of an electric cable is assumed to be a continuous randomm variable with probability density function f(x)-x-x), 0 Sx Sa a) What should the value of a be for f(x) to be a valid probability density function? points) b) Derive the cumulative distribution function of the random variable X c) Compute the expected value and variance of the random variable d) Compute a number b such that Pi(X s b) 2PtX 2 b). c) Coinpuk: the (xiidiinal probability lyx : 0.5 | 173 X.; 2

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But as χ>о, а:/ 329-29 こ0.5

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