Homework 4 Solutions.pdf - STAT 225 Spring 2018-Homework 4 SOLUTIONS 1 Desertland Hospital in Arizona keep records of its emergency room traffic Those

Homework 4 Solutions.pdf - STAT 225 Spring 2018-Homework 4...

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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. ?.
2
b)Write out the CDF for ?𝑋(?).
?? −
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c)What’s the probability X< 1.5? e)Find the probability that Xis more than 1.7.
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f)Given X< 1.9, what’s the probability that X<1.5?

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