1.

Let the discrete random variable X represent the number of tests needed by a doctor to diagnose a rare form of cancer. The probability distribution of X is shown below .r l '2 :3 4 .7) 6 T 1. (2 points) Fill in the question mark: P(X = 3) =? (show your math) 2. (2 points) Compute the expected value of X (show your math) 3. (2 points) What is the probability that it takes strictly more than 4 tests to get a diagnosis? 4. (2 points) If you pick a random (i.i.d.) sample of n = 3 patients, what is the probability that for all these patients it takes strictly more than 4 tests to get a diagnosis? (round the results to the 4th decimal place) 5. (2 points) If you pick a random (i.i.d.) sample of n = 3 patients, what is the probability that for exactly 1 (out of the 3 patients) it takes strictly more than 4 tests to get a diagnosis? 6. (2 points) The cost of diagnosing the rare form of cancer contains two components: the xed cost of using the facility is $100; the cost of each test is $25. What cost should the patient expect to pay