3.6 Practice Prelim Questions

3.6 Practice Prelim Questions - 20. A random variable X has...

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

View Full Document Right Arrow Icon
Review Problems for Prelim 3 Partial Derivatives Find ∂f/∂x and ∂f/∂y 1. ± x - y 2 2. (3 + 2 xy 2 ) 3 3. ln( x 2 + y 3 ) 4. y 2 e x 2 y 5. x 2 y x 2 + y 2 Find 2 f/∂x 2 and 2 f/∂y∂x 6. x 4 + x 2 y 2 + xy 3 + y 4 7. x y - y x 8. xe y/x De±nite Integrals (includes Improper Integrals) Volume problems turn into these after you use V = ² b a πf ( x ) 2 dx 9. ² 25 4 1 x dx 10. ² 0 x (1 + x ) - 5 / 2 dx 11. ² 3 2 8 x ( x 2 - 4) 3 dx 12. ² 2 1 2 x 2 +1 x dx 13. ² 2 0 2 x x 2 +1 dx 14. ² 2 0 6 x 3 2 x 2 +1 dx 15. ² 4 1 ln x x dx 16. ² e 1 ln x x dx 17. ² 1 e - 2 x x dx 18. ² 0 x 3 e - x 2 / 2 dx Probability Density Problems 19. A random variable X has density function 12 x 2 (1 - x ), Y has density function 12 x (1 - x ) 2 . Compute their means and variances. If you do this correctly then the means will add to 1 and the variances will be the same, since X and 1 - Y have the same distribution.
Background image of page 1

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

View Full DocumentRight Arrow Icon
Background image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 20. A random variable X has probability density f ( x ) = (1 / 7)(1 + 2 x-1 / 2 ) for 1 ≤ x ≤ 4. Find the mean and variance of X . 1 21. Suppose that baseball player salaries in units of hundreds of thousands of dollars have a probability density f ( x ) = cx-9 / 4 for x ≥ 1. (a) Find the constant c to make this a probability density. (b) What fraction of players make more than 10 million dollars (100 hundred thousand) (c) Find the average players salary. (d) Find the variance. 2...
View Full Document

This note was uploaded on 11/14/2007 for the course MATH 1106 taught by Professor Durrett during the Spring '07 term at Cornell.

Page1 / 2

3.6 Practice Prelim Questions - 20. A random variable X has...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online