hw13 - CS 70 Discrete Mathematics for CS Spring 2005...

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Unformatted text preview: CS 70 Discrete Mathematics for CS Spring 2005 Clancy/Wagner HW 13 Due Tuesday, May 10 Coverage: This assignment involves topics from the lectures of April 26 and May 3, and from Rosen section 3.2 (pages 233-236). Administrative reminders: We will accept only unformatted text files or PDF files for homework sub- mission. Include your name, login name, section number, and partner list in your submission. Give the command submit hw13 to submit your solution to this assignment. Homework exercises: 1. (10 pts.) Using standard units Let Z be a random variable that has a normal distribution with mean 0 and variance 1. Given a real number z , there are tables that allow us to compute Pr [ Z ≥ z ] as a function of z . The value z is sometimes called a z-score. For example: • The “right tail”: Pr [ Z ≥ 1 ] ≈ . 1587. Pr [ Z ≥ 2 ] ≈ . 0228. The right tail is the area under the normal curve represented by all values greater than or equal to z . • The “left tail”: Pr [ Z ≤- 1 ] ≈ . 1587. The left tail represents the values less than or equal to- z . You can find resources for calculating these values—e.g., normal tables, normal calculators—at http: //www.cs.berkeley.edu/˜daw/teaching/cs70-s05/tables.html . These allow you to go back and forth between a z-score z and the area under the standard normal curve represented by all values greater than z (the “right tail”), or the corresponding area represented by all values less than z (the “left tail”). (a) Let Z be normally distributed with mean 0 and variance 1. Use one of the tables or calculator mentioned above to find the approximate value of Pr [ Z ≥ 3 ] ....
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This note was uploaded on 09/03/2011 for the course CS 70 taught by Professor Papadimitrou during the Fall '08 term at Berkeley.

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hw13 - CS 70 Discrete Mathematics for CS Spring 2005...

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