Midterm 2 - (a) For what real numbers does there exist a...

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
Stat 5101 Second Midterm Exam November 12, 2008 Name Student ID The exam is closed book and closed notes. You may use one 8 1 2 × 11 sheet of paper with formulas, etc. You may also use the handouts on “brand name distributions” and Greek letters. Put all of your work on this test form (use the back if necessary). Show your work or give an explanation of your answer. No credit for numbers with no indication of where they came from. The points for the questions total to 100. There are 5 pages and 6 prob- lems. 1. [20 pts.] Suppose X is a random variable having probability density func- tion (PDF) given by f ( x ) = 6 5 ( x + x 2 ) , 0 < x < 1 . (a) Calculate E ( X ). (b) Calculate var( X ). 1
Background image of page 1

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

View Full DocumentRight Arrow Icon
2. [20 pts.] Suppose X is a random variable having PDF given by f ( x ) = 2 x 3 , 1 < x < . Find the PDF of the random variable Y = log( X ). 2
Background image of page 2
3. [20 pts.]
Background image of page 3

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

View Full DocumentRight Arrow Icon
Background image of page 4
Background image of page 5
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: (a) For what real numbers does there exist a constant c ( ) such that the function f ( x ) = c ( ) x , x &gt; 1 is a PDF? (b) Suppose is such that f is a PDF. If X is a random variable having this PDF, for what positive real numbers does E ( X ) exist? 3 4. [10 pts.] Calculate the PDF corresponding to the DF F ( x ) = , x ( x + x 2 ) / 2 , &lt; x &lt; 1 1 , x 1 5. [10 pts.] Calculate the DF corresponding to the PDF f ( x ) = cos( x ) 2 ,- 2 &lt; x &lt; 2 Dene the DF on the whole real line. 4 6. [20 pts.] Suppose the random variable X has the PDF (not the DF) given by f ( x ) = 2 x, &lt; x &lt; 1 . Find the median (not the mean) of the distribution of X . 5...
View Full Document

This note was uploaded on 10/28/2010 for the course STAT 5101 taught by Professor Staff during the Spring '02 term at Minnesota.

Page1 / 5

Midterm 2 - (a) For what real numbers does there exist a...

This preview shows document pages 1 - 5. Sign up to view the full document.

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