A continuous random variable has the following pdf: f(x)=c(x^2) if 0

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Transcript of A continuous random variable has the following pdf: f(x)=c(x^2) if 0

Page 1: A continuous random variable has the following pdf: f(x)=c(x^2) if 0
Page 2: A continuous random variable has the following pdf: f(x)=c(x^2) if 0

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 75th Percentile of x

Page 3: A continuous random variable has the following pdf: f(x)=c(x^2) if 0

• 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?

Page 4: A continuous random variable has the following pdf: f(x)=c(x^2) if 0

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?

Page 5: A continuous random variable has the following pdf: f(x)=c(x^2) if 0

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.

Page 6: A continuous random variable has the following pdf: f(x)=c(x^2) if 0

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?

Page 7: A continuous random variable has the following pdf: f(x)=c(x^2) if 0

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?

Page 8: A continuous random variable has the following pdf: f(x)=c(x^2) if 0

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?

Page 9: A continuous random variable has the following pdf: f(x)=c(x^2) if 0

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?


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