2.  A continuous random variable has the following pdf:  f(x)=c(x^2) if 0<x<3.  1. Find the value of c that makes f(x) a valid pdf.  2. Find the CDF of x.  3. Find P(x>2)  4. Find 75 th Percentile of x

3. A company manufactures a type of bulb whose life spreads evenly between 2000 to 2400 hours. They have a warranty on their bulbs and it states that if a bulb dies before 2300 hours, they will reimburse the customer $2.5 for each hour short of 2300. The cost of processing such a reimbursement is about $15. 1. What is the probability that the company is faced with a warranty liability of more than $255?

4.  2. On average, how much does the company expect to pay for the warranty cost of each bulb?  3. Let X be the amount of warranty cost to the company for each bulb, what is the pdf of X?

5.  You have ordered something online and there are two shipping options: if you choose to use USPS, the delivery time varies uniformly between 1 day to 5 days; if you use UPS, it follows an exponential distribution with a mean time of 3 days. Which option will you choose and state your reason.

6.  Your friend is looking for a job and has submitted a resume at a company’s website. Usually, the time an applicant has to wait for a callback follows an exponential distribution with a mean of 5 days.  1. What is the probability that your friend gets a callback within 3 days of submitting the resume?

7.  2. What is the probability that your friend has to wait for more than 7 days to get a callback?  3. It has been 4 days and your friend still has not got a call back, what is the probability that he will not get a callback after day 5?

8.  10 days after submission, you asked your friend and he told you that he already got a callback, what is the probability that he receives the call back within 5 days?

9.  A doctor has received 200 patients with flu symptoms. With appropriate prescription, those symptoms should be gone in 7 days for an average patient. What is the probability that 20% of his patients still have the symptoms after 10 days?