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Q7) The diameter of an electric cable, say X, is assumed to be a continuous random variable with probability density function given by f(x) =

Q7) The diameter of an electric cable, say X, is assumed to be a continuous random

variable with probability density function given by f(x) = {kx (1-x), 0

(1) Find the value of k.

(ii) Determine a number such that P(X< b) = P(x > b).

(iii) Find the mean and variance of the random variable X.

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