{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# Handout9 - of X 2 For Example 3 ±nd E Y 3 For Example 1...

This preview shows pages 1–2. Sign up to view the full content.

STOR 435 Handout 9 Sections 5.1-5.3 Example 1 (Example 1a; Continuous rv) . Suppose X is a random variable whose pdf is given by f ( x ) = braceleftbigg C (4 x - 2 x 2 ) 0 <x< 2 0 otherwise 1. Find C 2. What is P ( X > 1)? 3. What is P ( X = 1)? Example 2 (Example 1c; Continuous rv) . The lifetime in hours of a particular radio tube is a random variable having pdf f ( x ) = braceleftbigg 0 x 100 100 /x 2 x> 100 Suppose a radio has 5 tubes, the lifetime of each of the radio tubes having the above distribution. What is the probability that exactly 2 out of the 5 radio tubes will have to be replaced within the first 150 hours of operation? You can assume that E i ,i = 1 , 2 , 3 , 4 , 5, the events that the i th tube has to be replaced within 150 hours are independent of each other. Example 3. For a particular computer component, the lifetime of the compo- nent in hours is known to have density f ( x ) = 10 <x< 1 Let the random variable Y = e X . What is the pdf of Y ? Example 4 (Expectations)

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: of X 2. For Example 3, ±nd E ( Y ) 3. For Example 1 ±nd var ( X ) Example 5 (Exercise 5.10; Uniform distribution) . Trains headed for destina-tion A arrive at the train station at 15- minute intervals starting at 7 A. M., whereas trains headed for destination B arrive at 15-minute intervals starting at 7: 05 A. M. 1 1. If a certain passenger arrives at the station at a time uniformly distributed between 7 and 8 A. M. and then gets on the Frst train that arrives, what proportion of time does he or she go to destination A? 2. What if the passenger arrives at a time uniformly distributed between 7: 10 and 8: 10 A. M.? 3. ±or part(a) if X denotes the number of minutes after 7 that the passenger arrives what is E ( X )? What is var ( X )? 2...
View Full Document

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern