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cs-401r:assignment-1.5 [2014/09/24 21:41]
cs401rPML [Question 1: Useful theorems in probability theory] added link to example proofs page
cs-401r:assignment-1.5 [2014/09/26 01:49] (current)
ringger [Question 1: Useful theorems in probability theory]
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 (Adapted from: Manning & Schuetze, p. 59, exercise 2.1) (Adapted from: Manning & Schuetze, p. 59, exercise 2.1)
  
-Use the [[Set Theory Identities]] and [[Axioms of Probability Theory]] to prove each of the following statements. ​ Develop your proof first in terms of sets and then translate into probabilities;​ use set theoretic operations on sets and arithmetic operators on probabilities. ​ Be sure to apply [[Proofs|good proof technique]]:​ justify each step in your proofs; set up your proofs in two-column format, with each step showing a statement on the left and a justification on the right. Remember that in order to invoke an axiom as justification,​ you must first satisfy the conditions / pre-requisites of the axiom. See the proofs on the [[example_proofs|example proofs page]].+Use the [[Set Theory Identities]] and [[Axioms of Probability Theory]] to prove each of the following statements. ​ Develop your proof first in terms of sets and then translate into probabilities;​ use set theoretic operations on sets and arithmetic operators on probabilities. ​ Be sure to apply [[Proofs|good proof technique]]:​ justify each step in your proofs; set up your proofs in two-column format, with each step showing a statement on the left and a justification on the right. Remember that in order to invoke an axiom as justification,​ you must first satisfy the conditions / pre-requisites of the axiom. ​(See the [[example_proofs|example proofs page]] ​for one example.)
 # $P(\varnothing) = 0$ # $P(\varnothing) = 0$
 # $A \subseteq B \Rightarrow P(A) \leq P(B)$ # $A \subseteq B \Rightarrow P(A) \leq P(B)$
cs-401r/assignment-1.5.txt ยท Last modified: 2014/09/26 01:49 by ringger
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