homework1a - Math 418 Assignment 1–due Wed. Sept. 23...

Info iconThis preview shows pages 1–2. 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: Math 418 Assignment 1–due Wed. Sept. 23 Final Version. N denotes the set of natural numbers. 1. A poker hand has two pair if it contains two cards of one rank, two cards of a second distinct rank and a last card of a third and distinct rank. Find P (two pair and the hand has all cards of the same colour) . 2. Let Ω = N and F = { A ⊂ N : A or A c is finite } . (a) Show that F is a field but not a σ-field of subsets of Ω. (b) For A ∈ F , define P ( A ) = braceleftBig if A is finite 1 if A c is finite. Prove that P : F → [0 , 1] is finitely additive but not countably additive on F . Here we say P is countably additive on a field F iff whenever { A n } is a sequence of disjoint sets in F whose union is in F then P ( ∪ A n ) = summationdisplay n P ( A n ) . 3. A factory has two machines A and B that make 60% and 40% of the total production, respectively. Of their output, machine A produces 3% defective items, while machine B produces 5% defective items. Find the probability that a give defective part was producedproduces 5% defective items....
View Full Document

Page1 / 2

homework1a - Math 418 Assignment 1–due Wed. Sept. 23...

This preview shows document pages 1 - 2. Sign up to view the full document.

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