6.1 Given a continuous uniform distribution, show that (a) ,u: A%B and 2 _ (Bi/U2 (b) 0 T~ 6.2 Suppose X follows a continuous uniform distribu tion from 1 to 5. Determine the conditional probability P(X> 2.5 l X 34). Additional question (0) What is the probability that the individual waits more than 7 minutes today and waits less than 7 minutes tomorrow? Assume that the waiting time on each day is independent. Problem 1. A certain type of storage battery lasts. on average, 3.0 years with a standard deviation of 0.5 year. Assuming that battery life is normally distributed, nd the following probabilities: Use 68-95-997 rule. Draw a normal curve to identify the corresponding areas. (a) a randomly selected battery will last more than 2 years but less than 2.5 years. (b) a randomly selected battery will last less than 3.5 years