Question: The random variable X has the following probability distribution. (a) Is this probability distribution valid? Explain and list the requirements for a valid probability distribution.

The random variable X has the following probability distribution. (a) Is this probability distribution valid? Explain and list the requirements for a valid probability distribution. C Yes, f(x) 2 0 and 2f(x) at 1 C Yes, f(x) 2 0 and Ef(x) = 1 C No, f(x) 2 0 and 2f(x) 4: 1 C No, f(x) 2 0 and 2f(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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