10. The probability distribution below is for the random variable X = the number of credits taken by a randomly selected first-year student at a large state university. Credits 14 15 16 17 Probability 0.05 0.65 0.20 0.10 (a) Is X a discrete or a continuous random variable? Explain. (b) Show that the probability distribution of X is valid. (c) Make a histogram of the probability distribution. Describe its shape. (d) Compute and interpret the expected value of X. Show work. (e) The standard deviation is 6.43. Interpret this value in the context of the problem. (f) Express the event "taking at least 16 credits" in terms of X and find its probability