Exam 01 practice

Important

This page contains practice problems to help prepare for Exam 01. This set of practice problems is not comprehensive.

There is no answer key for these problems, however, some might be discussed in review session. You may ask questions in office hours and on Ed Discussion.

Question 1

A box contains 6 red balls and 4 blue balls. If you pick 3 balls at random without replacement, \(Y\) is the total number of red balls you get from these 3 picks. \(X_i\) is the ball of the \(i\)-th pick. \(X_i\) equal to 1 if the \(i\)-th pick is a red ball, otherwise 0.

Determine the value of the following:

  1. \(P(X_2\mid X_1=0)\) and \(P(X_2\mid X_1=1)\)

  2. \(P(X_2=1)\) and \(P(X_3=1)\)

  3. \(P(X_2=1\mid X_3=0)\)

  4. \(P(Y=2)\)

  5. \(E(Y)\)

Relevant lectures and assignments

Ask yourself “why” questions as you review the slides, review your answers, process, and derivations on these assignments. It may also be helpful to explain your process to others.

  • Lectures: August 18 - September 8 (September 8 lecture is an exam review)

  • HW 01 - 02