The random variable x has the following probability distribution. x f(x) 0 1 0.25 0.15 2 0.15 3 4 0.20 0.25 (a) Is this probability distribution valid? Explain and list the requirements for a valid probability distribution. O Yes, f(x) > 0 and Ef(x) = 1 Yes, f(x) > 0 and £f(x) = 1 O No, f(x) > 0 and Σf(x) = 1 O No, f(x) > 0 and Ef(x) = 1 (b) Calculate the expected value of x. (c) Calculate the variance of x. (d) Calculate the standard deviation of x. (Round your answer to four decimal places.)

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