{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

131A_1_ds1_sol_2010fall

# 131A_1_ds1_sol_2010fall - EE 131A Probability Instructor...

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

EE 131A Discussion Set 1 Probability Wednesday, September 29, 2010 Instructor: Lara Dolecek and Friday, October 1, 2010 Reading: Chapter 2 of Probability, Statistics, and Random Processes by A. Leon-Garcia 1. Venn diagram. Problem 2.13, page 82 of ALG Solution : Using the Venn diagram in Figure 1, the event “exactly one of the events A and B occurs” can be expressed as ( A B c ) ( A c B ) Figure 1: Decomposition of A B into three disjoint sets. 2. Balls and buckets. Problem 2.50, page 86 of ALG Solution : The possible ways to cover all the buckets =5! The possible placements of 5 balls in 5 buckets=5 5 Therefore,the probability that each bucket has a ball= 5! 5 5 3. Bonferroni’sinequality. Suppose A and B are two events. Use the axioms of probability to prove the following: P ( A B ) P ( A ) + P ( B ) - 1 Proof : Using Corollary 5, P ( A B ) = P ( A ) + P ( B ) - P ( A B ) Using Corollary 2, P ( A B ) 1 Therefore, P ( A ) + P ( B ) - P ( A B ) 1 = P ( A B ) P ( A ) + P ( B ) - 1 Show that the probability that one and only one of the events A or

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}