EL630 HW1 - EL630: Homework 1 1. (Book; 2-1) Show that ( a...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

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

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

Unformatted text preview: EL630: Homework 1 1. (Book; 2-1) Show that ( a ) A +B + A +B =A ; (b) ( A+B ) AB =AB +B A . (Hint: Use De Morgan’s Law A + B = AB, AB = A + B ) (Book: 2-2) If A = {2 ≤ x ≤ 5}and B = {3 ≤ x ≤ 6},find A + B, AB,and ( A + B ) AB . 2. 3. (Book: 2-3) Show that if AB = {∅}, then P ( A) ≤ P ( B ). B A (Hint: In order to do this type of theoretical problems, you have to first understand the proofs of those four properties of probability in this lecture.) 4. (Book :2 − 4,) Show that (a ) if P ( A) = P ( B ) = P ( AB ), then P ( AB + B A) = 0; (b) if P ( A) = P ( B) = 1, then P ( AB ) = 1. 1 AB AB AB (Hint: Try to first understand the proof of the last Theorem in Lecture 1, and notice that: A + B = AB + AB + AB, and AB, AB and AB are mutually exclusive.) 5. (Book :2 − 5) Prove thefollowing identity P ( A + B + C ) = P( A) + P ( B ) + P (C ) − P ( AB ) − P ( AC ) − P ( BC ) + P ( ABC ) A C B 6. A ⊂ B.Find P ( A + B ) and P ( AB )in terms of P ( A) and P ( B ). B A 2 7. What is the probability that, in New York City, there are at least two people with the same number of hairs on the head? 8. Randomly cut a line segment into three pieces. What is the probability that these three pieces can form a triangle? 0 1 3 ...
View Full Document

Page1 / 3

EL630 HW1 - EL630: Homework 1 1. (Book; 2-1) Show that ( a...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online