(2 points) A fax machine dials a phone number that is typica…

(2 points) A fax machine dials a phone number that is typically busy 80% of the time. The machine dials it every 5 minutes until the line is clear and the fax is able to be transmitted. What is the probability that the fax machine will have to dial the number 9 times?

(4 points) Suppose it is known that 0.001% of the general po…

(4 points) Suppose it is known that 0.001% of the general population has certain type of cancer. A patient visits a doctor complaining of symptoms that might indicate the presence of this cancer. The doctor performs a blood test that will confirm the cancer with the probability of 0.99 if the patient does indeed have cancer. However, the test also produces false positives or says a person has cancer when they do not. The occurs with the probability of 0.2. If the test comes back positive, what is the probability that the person has cancer?

True or False: The ACF values from the ACF plot for a given…

True or False: The ACF values from the ACF plot for a given data provide unbiased estimates of the true autocorrelations for each lag h. Therefore we can rely on the sample estimate to reflect the real autocorrelation from the ACF plot even when h is approaching sample size n. 

(2 points) An urn contains 3 red balls and 2 black balls. Tw…

(2 points) An urn contains 3 red balls and 2 black balls. Two balls are chosen in succession. The first ball is returned to the urn before the second ball is chosen. Each ball is chosen at random, which means that we are equally likely to choose any ball. (1 point) What is the probability of choosing first a red ball and then a black ball? (1 point) More generally, if the urn has red balls and