A group of patients with a potentially fatal disease has been treated with an experimental drug. Assume the survival time X for a patient receiving the drug is a random variable exponentially distributed with density function

where x is the number of years a patient survives after first receiving the drug.

a. Research indicates that the expected survival time for a patient receiving the drug is 5 years. Based on this information, what is k?

b. Using the density function determined in part (a), what is the probability that a randomly selected patient survives for less than 2 years?

c. What is the probability that a randomly selected patient survives for more than 7 years?

Transcribed Image Text:

f(x) = -kx Ske lo if x ≥ 0 if x < 0