This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Math 55: Midterm #2, 3 March 2008 Write your name, your student ID number, your section time and number, and a threeproblem grading grid, on the cover of your blue book. Hand in your exam book at 11:00 am. Books, notes, calculators, scratch paper and/or collaboration are not allowed. Justify your computations: correct answers with inadequate explanation may receive partial credit. 1: Five pecans p 1 , p 2 , p 3 , p 4 and p 5 are given to three squirrels s 1 , s 2 and s 3 , with each pecan given to one squirrel chosen independently with equal probabilities. (a) Describe the sample space and compute its cardinality. (b) Compute the probability that the first squirrel s 1 gets all the pecans. (c) Compute the expected number of pecans the last squirrel s 3 gets. (d) Compute the variance of the number of pecans the last squirrel gets. (e) Compute the probability that each squirrel gets at least one pecan. 2: A discrete math midterm consists of 19 independent truefalse questions on Martian literature. On each question, any nonMartian student has a 1 / 3 chance of guessing the correct answer. Two students (in the class of 28 students) are Martian, and therefore will get perfect scores. (a) What is the probability that a student chosen at random from the non Martian students gets a perfect score? (b) What is the probability that a student chosen at random from the whole class gets a perfect score? (c) Given that a student named Z rthjkpq got a perfect score on the midterm, compute the probability that Z rthjkpq is a Martian. 3: For any integer k 0, let T k be the set of all k letter strings of X s, Y s and Z s that HAVE two consecutive X s. For example, T 3 = { XXY, XXZ, Y XX, ZXX, XXX } ....
View
Full
Document
 Fall '08
 STRAIN
 Math

Click to edit the document details