Suppose that a new drug is being investigated to combat some form of cancer. In phase II trials, researchers look for evidence that the drug will improve survival by first seeing if it can reduce the size of a patient’s tumours by at least 50%. If a patient’s tumors do decrease by 50% after taking the drug, the patient is said to respond or be a responder. Assume that the population of patients eligible for the trial is very large and we intend to randomly draw 10 names of eligible patients and include them in the clinical trial. If the true probability of a response is equal to 0.4,
a) define the random variable X for this problem.
b) write down the appropriate probability mass function for X, indicating the support of X.
c) what is the chance that exactly 6 of the 10 patients respond to the new drug?
d) what is the probability that at least 80% of the patients respond to the new drug?
e) calculate the expected number of responders.
f) find the standard deviation of the number of responders.