Question: 8. We choose a number from the set {10, 11, 12, ..., 99} uniformly at random. (a) Let X be the first digit and

8. We choose a number from the set {10, 11, 12, ...,

8. We choose a number from the set {10, 11, 12, ..., 99} uniformly at random. (a) Let X be the first digit and Y the second digit of the chosen number. Show that X and Y are independent random variables. (b) Let X be the first digit of the chosen number and Z be the sum of the two digits. Show that X and Z are not independent.

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