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The random variable x has the following probability distribution. 0.15 1 0.20 0.25 0.25 0.15 (a) Is this probability distribution valid? Explain and list the requirements for a valid probability distribution. Yes, (x) 2 0 and Er(x) = 1 Yes, (x) 2 0 and Er(x) = 1 O No, (x) 2 0 and En(x) = 1 No, (x) 2 0 and En(x) = 1 (b) Calculate the expected value of x. 2.05 (c) Calculate the variance of x. 1.6475 [d) Calculate the standard deviation of x. (Round your answer to four decimal places.) 1.2835