Practice1 - Practice problems for Midterm 1 Problem 1 You...

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

View Full Document Right Arrow Icon
Practice problems for Midterm 1 Problem 1 You are given two coins, one fair and the second one that comes up heads with probability . 7. Initially, you have no information which coin is biased (the two coins look the same). You toss each of the two coins twice, and coin A comes up heads more times than coin B does. What is the probability that coin A is the biased one? Problem 2 The pdf of a continuous random variable X is given by f X ( x ) = ± a if 0 < x < 1 b if - 1 < x < 0 . The random variable has the mean EX = 1 / 4. ( a ) Find a and b and plot the density. ( b ) Compute and plot the cumulative distribution function of X . ( c ) Find P ( X 1 / 2), P ( X = - 2 / 3) and P ( X = 0). Problem 3 A continuous random vector ( X,Y ) has a joint pdf given by f X,Y ( x,y ) = ± 6 y if 0 < y < 1 and y < x < 2 - y 0 otherwise . ( a ) Find the marginal probability densities of X and Y . Are X and Y independent? ( b
Background image of page 1

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

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

This note was uploaded on 10/29/2011 for the course MATH 3310 at Cornell University (Engineering School).

Page1 / 3

Practice1 - Practice problems for Midterm 1 Problem 1 You...

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