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# PROB & STATISTICS PSTAT 120A

UCSB

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This 2 page Class Notes was uploaded by Douglas Simonis on Thursday October 22, 2015. The Class Notes belongs to PSTAT 120A at University of California Santa Barbara taught by Staff in Fall. Since its upload, it has received 64 views. For similar materials see /class/226912/pstat-120a-university-of-california-santa-barbara in Statistics and Probability at University of California Santa Barbara.

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Date Created: 10/22/15

Chapter 1 Terms Subset An event E is said to be a subset of the event F if whenever E occurs F also occurs All the sample points ofE are contained in F Denoted as E E F Eguality Events E and F are said to be equal if the occurrence of E implies the occurrence of F and vice versa IfE E F and F E E then E F Intersection An event is called an intersection of two events E and F if it occurs only whenever E and F occur simultaneously This is denoted as E n F Union An event is called the union of two events E and F if it occurs whenever at least one of them occurs All the points in this event denoted E U F are in E or F or both Difference An event is called the difference of two events E and F if it occurs whenever E occurs but F does not The difference ofthe events E and F is denoted b E F FC SF and E F E nFc Certainty An event is called certain is its occurrence is inevitable Thus the sample space is a certain event Impossibility An event is called impossible if there is certainty in its nonoccurrence Therefore the empty set 0 which is SC is an impossible event Mutual Exclusiveness If the joint occurrence of two events E and F is impossible E and F are mutually exclusive This is denoted by E n F 0 A set of events E1 E2 is called mutually exclusive if and only if every pair of events is mutually exclusive Laws Commutative E U F F U E E n F F n E Associative EUFUGEUFUG EnFnGEnFnG Distributive EnFUGEUGnFUG EnFnGEnGUFnG De Morgans EUFCECnFC E n Fc 3 o F6 g EE 1 l Axiom 1PA 2 0 Axiom 2PS 1 Axiom 3For a sequence of mutually exclusive events the probability of the occurrence of at least one of them is equal to the sum of their probabilities Theorems Theorem 11 PUD 0 9 Probability of the empty set is zero Theorem 12 If A and B are mutually exclusive then PA u B PA PB Theorem 13 For any event A of Sample space S where S has N points that are all equally likely to occur PA NA N where NA is the number ofpoints ofA

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