STAT 225 Spring 2018--Homework 4 ---SOLUTIONS 1.Desertland Hospital in Arizona keep records of its emergency room traffic. Those records indicate that, beginning at 6:00 PM on any given day, the average time until a patient arrives is 10.2 minutes. Each patient arrival is independent. a)On a particular day, what is the probability the first patient arrives before 6:15 PM? What distribution and parameter(s) are you using?
b)What is the probability that first patient arrives after 6:08 PM?
c)What is the probability that the first patient arrives between 6:15 PM and 6:30 PM?
d)Given a patient arrives after 6:10 PM, what is the probability the first patient arrives before 6:21 PM?
e)Find the median time to the first arrival. What time is that on the clock?
2.X is a random variable with a probability density function given by: ?𝑋(?) = ?4for 1 ≤ ? < 2and 0 otherwisea)Determine the value of kto make this a valid probability density function. ?.
b)Write out the CDF for ?𝑋(?).