5. Suppose the time required for a processor to complete a set of four jobs may be modeled by a Gamma density. The average amount of time it takes is 2 hours, and the SD is 1 hour. a) Find a and 2. What is the average amount of time needed for one job? b) Set up the probability density function. c) Use several iterations of integration by parts to find an antiderivative of the density. (You may want to use the tabular method of integration by parts.) d) Using part (c), find the probability that the processor will take less than 1 hour to complete the next set of four jobs. e) Using part (c), find the probability that the processor will require more than 3 hours to complete the next set of four jobs.

Directions: The amount of time required to serve a customer at a bank has an exponential density function with mean 4 minutes. 1. Find the probability that a customer is served in less than 3 minutes. Probability = 2. Find the probability that serving a customer will require more than 6 minutes. Probability =

Consider a group of people who have received treatment for a disease such as cancer. Let t be the survival time, the number of years a person lives after receiving treatment. The density function giving the distribution of t is p(t) = Ce-Ct for some positive constant C, and the cumulative distribution function is P(t) = , p(x)dx. Think carefully about what the practical meaning of P(t) is, being sure that you can put it into words. a) The survival function, S(t), is the probability that a randomly selected person survives for at least t years. Find a formula for S(t). b) Suppose that a patient has a 80 percent chance of surviving at least 2 years. Find C. c) Using the value of C you found in (b), find the probability that the patient survives up to (that is, less than or equal to) 1 years. d) Using the value of C you found in (b), find the the mean survival time for patients with this survival function, in years.

Hi. Please help. I need to calculate the mean and vairance of the probabiltiy density function I am getting one minute but the time better each serving is at least 2 minutes. Can you correct me as I have gone wrong somewhere. (see attached doc)