5. Let X be a discrete random variable. The following table shows its possible values x...

 

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5. Let X be a discrete random variable. The following table shows its possible values x and the associated probabilities P(X = x) = f(x). I -1 0 1 3 (x) 2/8 3/8 2/8 1/8 (a) Verify that f(x) is a probability mass function. (b) Calculate P(X < 1), P(X ≤ 1), and P(X < 0.5 or X > 2). (c) Find the cumulative distribution function of X. (d) Compute the mean and the variance of X. 5. Let X be a discrete random variable. The following table shows its possible values x and the associated probabilities P(X = x) = f(x). I -1 0 1 3 (x) 2/8 3/8 2/8 1/8 (a) Verify that f(x) is a probability mass function. (b) Calculate P(X < 1), P(X ≤ 1), and P(X < 0.5 or X > 2). (c) Find the cumulative distribution function of X. (d) Compute the mean and the variance of X.