. Suppose the probability of selecting a number from the interval [0, 2] is given by f(x) = Cx. (a) Find the value of C so that this is a probability distribution. (b) Find the probability that the given number is in the interval [0,1]. Now find the probability that the selected number is in the interval [1, 2]. The answers differ. Why? (c) If X (x) = x is the random variable giving the value of the selected number, what is E(X)? The Var(X)?

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