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SFSU / Mathematics / MATH 124 / What is the equation of continous random variables?

What is the equation of continous random variables?

What is the equation of continous random variables?

Description

School: San Francisco State University
Department: Mathematics
Course: Elementary Statistics
Professor: Van tran
Term: Summer 2015
Tags: Statistics
Cost: 25
Name: Week 9- Elementary Statistics
Description: These notes cover: -Continuous Random Variables -Probability (and the 5 rules) 10-17-16 & 10-19-16
Uploaded: 11/08/2016
9 Pages 147 Views 1 Unlocks
Reviews


ul.lst-kix_jvm48z9p7qom-1{list-style-type:none}.lst-kix_lrnabi51sw2p-1 > li{counter-increment:lst-ctn-kix_lrnabi51sw2p-1}ul.lst-kix_jvm48z9p7qom-2{list-style-type:none}ul.lst-kix_jvm48z9p7qom-3{list-style-type:none}ul.lst-kix_jvm48z9p7qom-4{list-style-type:none}ul.lst-kix_jvm48z9p7qom-0{list-style-type:none}ol.lst-kix_k3xb21291put-1.start{counter-reset:lst-ctn-kix_k3xb21291put-1 0}ul.lst-kix_jvm48z9p7qom-5{list-style-type:none}ul.lst-kix_jvm48z9p7qom-6{list-style-type:none}ul.lst-kix_jvm48z9p7qom-7{list-style-type:none}ul.lst-kix_jvm48z9p7qom-8{list-style-type:none}ol.lst-kix_lrnabi51sw2p-0.start{counter-reset:lst-ctn-kix_lrnabi51sw2p-0 0}ol.lst-kix_i1ngeq9ml73k-3.start{counter-reset:lst-ctn-kix_i1ngeq9ml73k-3 0}.lst-kix_i1ngeq9ml73k-1 > li{counter-increment:lst-ctn-kix_i1ngeq9ml73k-1}ul.lst-kix_2ziulcxtjgb3-2{list-style-type:none}ul.lst-kix_2ziulcxtjgb3-3{list-style-type:none}ul.lst-kix_2ziulcxtjgb3-0{list-style-type:none}ul.lst-kix_2ziulcxtjgb3-1{list-style-type:none}ul.lst-kix_2ziulcxtjgb3-6{list-style-type:none}ul.lst-kix_2ziulcxtjgb3-7{list-style-type:none}ul.lst-kix_2ziulcxtjgb3-4{list-style-type:none}ul.lst-kix_2ziulcxtjgb3-5{list-style-type:none}ul.lst-kix_2ziulcxtjgb3-8{list-style-type:none}.lst-kix_sputu5pju21l-2 > li:before{content:"- "}.lst-kix_sputu5pju21l-3 > li:before{content:"- "}.lst-kix_lrnabi51sw2p-8 > li:before{content:"" counter(lst-ctn-kix_lrnabi51sw2p-8,lower-roman) ". "}.lst-kix_sputu5pju21l-5 > li:before{content:"- "}.lst-kix_lrnabi51sw2p-7 > li:before{content:"" counter(lst-ctn-kix_lrnabi51sw2p-7,lower-latin) ". "}.lst-kix_sputu5pju21l-4 > li:before{content:"- "}.lst-kix_jvm48z9p7qom-8 > li:before{content:"- "}.lst-kix_sputu5pju21l-7 > li:before{content:"- "}.lst-kix_jvm48z9p7qom-5 > li:before{content:"- "}.lst-kix_jvm48z9p7qom-6 > li:before{content:"- "}.lst-kix_lrnabi51sw2p-3 > li{counter-increment:lst-ctn-kix_lrnabi51sw2p-3}.lst-kix_jvm48z9p7qom-7 > li:before{content:"- "}.lst-kix_sputu5pju21l-6 > li:before{content:"- "}ol.lst-kix_k3xb21291put-7.start{counter-reset:lst-ctn-kix_k3xb21291put-7 0}.lst-kix_ctsx5spatzhm-1 > li:before{content:"- "}.lst-kix_ctsx5spatzhm-3 > li:before{content:"- "}.lst-kix_sputu5pju21l-8 > li:before{content:"- "}.lst-kix_ctsx5spatzhm-2 > li:before{content:"- "}.lst-kix_um1rr2y18kam-0 > li:before{content:"- "}ol.lst-kix_k3xb21291put-6.start{counter-reset:lst-ctn-kix_k3xb21291put-6 0}ol.lst-kix_lrnabi51sw2p-5.start{counter-reset:lst-ctn-kix_lrnabi51sw2p-5 0}.lst-kix_ctsx5spatzhm-5 > li:before{content:"- "}.lst-kix_um1rr2y18kam-1 > li:before{content:"- "}.lst-kix_um1rr2y18kam-3 > li:before{content:"- "}.lst-kix_ctsx5spatzhm-4 > li:before{content:"- "}.lst-kix_um1rr2y18kam-2 > li:before{content:"- "}.lst-kix_um1rr2y18kam-5 > li:before{content:"- "}.lst-kix_2ziulcxtjgb3-1 > li:before{content:"- "}.lst-kix_2ziulcxtjgb3-3 > li:before{content:"- "}.lst-kix_i1ngeq9ml73k-8 > li{counter-increment:lst-ctn-kix_i1ngeq9ml73k-8}.lst-kix_ctsx5spatzhm-7 > li:before{content:"- "}.lst-kix_ctsx5spatzhm-6 > li:before{content:"- "}.lst-kix_um1rr2y18kam-4 > li:before{content:"- "}.lst-kix_um1rr2y18kam-8 > li:before{content:"- "}.lst-kix_2ziulcxtjgb3-0 > li:before{content:"- "}.lst-kix_2ziulcxtjgb3-4 > li:before{content:"- "}.lst-kix_um1rr2y18kam-7 > li:before{content:"- "}.lst-kix_ctsx5spatzhm-8 > li:before{content:"- "}.lst-kix_um1rr2y18kam-6 > li:before{content:"- "}.lst-kix_2ziulcxtjgb3-2 > li:before{content:"- "}ul.lst-kix_ctsx5spatzhm-2{list-style-type:none}ul.lst-kix_ctsx5spatzhm-1{list-style-type:none}ul.lst-kix_ctsx5spatzhm-4{list-style-type:none}ul.lst-kix_ctsx5spatzhm-3{list-style-type:none}ul.lst-kix_ctsx5spatzhm-6{list-style-type:none}.lst-kix_k3xb21291put-2 > li{counter-increment:lst-ctn-kix_k3xb21291put-2}ul.lst-kix_ctsx5spatzhm-5{list-style-type:none}ul.lst-kix_ctsx5spatzhm-8{list-style-type:none}ul.lst-kix_ctsx5spatzhm-7{list-style-type:none}ol.lst-kix_lrnabi51sw2p-6.start{counter-reset:lst-ctn-kix_lrnabi51sw2p-6 0}.lst-kix_i1ngeq9ml73k-5 > li{counter-increment:lst-ctn-kix_i1ngeq9ml73k-5}.lst-kix_k3xb21291put-5 > li{counter-increment:lst-ctn-kix_k3xb21291put-5}.lst-kix_ctsx5spatzhm-0 > li:before{content:"- "}ul.lst-kix_ctsx5spatzhm-0{list-style-type:none}ol.lst-kix_lrnabi51sw2p-0{list-style-type:none}ol.lst-kix_lrnabi51sw2p-7{list-style-type:none}ol.lst-kix_lrnabi51sw2p-8{list-style-type:none}ol.lst-kix_lrnabi51sw2p-5{list-style-type:none}ol.lst-kix_lrnabi51sw2p-6{list-style-type:none}ol.lst-kix_lrnabi51sw2p-3{list-style-type:none}ol.lst-kix_lrnabi51sw2p-4{list-style-type:none}ol.lst-kix_lrnabi51sw2p-1{list-style-type:none}ol.lst-kix_lrnabi51sw2p-2{list-style-type:none}.lst-kix_2ziulcxtjgb3-8 > li:before{content:"- "}ol.lst-kix_i1ngeq9ml73k-1.start{counter-reset:lst-ctn-kix_i1ngeq9ml73k-1 0}.lst-kix_k3xb21291put-0 > li:before{content:"" counter(lst-ctn-kix_k3xb21291put-0,decimal) ". "}ol.lst-kix_k3xb21291put-0.start{counter-reset:lst-ctn-kix_k3xb21291put-0 0}.lst-kix_2ziulcxtjgb3-6 > li:before{content:"- "}.lst-kix_k3xb21291put-4 > li:before{content:"" counter(lst-ctn-kix_k3xb21291put-4,lower-latin) ". "}ol.lst-kix_lrnabi51sw2p-1.start{counter-reset:lst-ctn-kix_lrnabi51sw2p-1 0}.lst-kix_lrnabi51sw2p-6 > li{counter-increment:lst-ctn-kix_lrnabi51sw2p-6}.lst-kix_i1ngeq9ml73k-6 > li{counter-increment:lst-ctn-kix_i1ngeq9ml73k-6}.lst-kix_e0nfih6q87yj-1 > li:before{content:"- "}ol.lst-kix_i1ngeq9ml73k-4.start{counter-reset:lst-ctn-kix_i1ngeq9ml73k-4 0}.lst-kix_k3xb21291put-2 > li:before{content:"" counter(lst-ctn-kix_k3xb21291put-2,lower-roman) ". "}ol.lst-kix_lrnabi51sw2p-4.start{counter-reset:lst-ctn-kix_lrnabi51sw2p-4 0}.lst-kix_jpaysgvdrnw2-1 > li:before{content:"- "}.lst-kix_i1ngeq9ml73k-5 > li:before{content:"" counter(lst-ctn-kix_i1ngeq9ml73k-5,lower-roman) ". "}.lst-kix_jvm48z9p7qom-2 > li:before{content:"- "}.lst-kix_lrnabi51sw2p-0 > li:before{content:"" counter(lst-ctn-kix_lrnabi51sw2p-0,decimal) ". "}.lst-kix_lrnabi51sw2p-2 > li:before{content:"" counter(lst-ctn-kix_lrnabi51sw2p-2,lower-roman) ". "}ol.lst-kix_k3xb21291put-0{list-style-type:none}.lst-kix_jpaysgvdrnw2-3 > li:before{content:"- "}.lst-kix_i1ngeq9ml73k-3 > li:before{content:"" counter(lst-ctn-kix_i1ngeq9ml73k-3,decimal) ". "}.lst-kix_i1ngeq9ml73k-7 > li:before{content:"" counter(lst-ctn-kix_i1ngeq9ml73k-7,lower-latin) ". "}.lst-kix_jvm48z9p7qom-0 > li:before{content:"- "}.lst-kix_jvm48z9p7qom-4 > li:before{content:"- "}.lst-kix_k3xb21291put-8 > li:before{content:"" counter(lst-ctn-kix_k3xb21291put-8,lower-roman) ". "}.lst-kix_k3xb21291put-6 > li{counter-increment:lst-ctn-kix_k3xb21291put-6}.lst-kix_lrnabi51sw2p-4 > li:before{content:"" counter(lst-ctn-kix_lrnabi51sw2p-4,lower-latin) ". "}.lst-kix_lrnabi51sw2p-6 > li:before{content:"" counter(lst-ctn-kix_lrnabi51sw2p-6,decimal) ". "}.lst-kix_e0nfih6q87yj-3 > li:before{content:"- "}.lst-kix_k3xb21291put-1 > li{counter-increment:lst-ctn-kix_k3xb21291put-1}.lst-kix_k3xb21291put-6 > li:before{content:"" counter(lst-ctn-kix_k3xb21291put-6,decimal) ". "}.lst-kix_k3xb21291put-7 > li{counter-increment:lst-ctn-kix_k3xb21291put-7}.lst-kix_e0nfih6q87yj-5 > li:before{content:"- "}.lst-kix_e0nfih6q87yj-7 > li:before{content:"- "}.lst-kix_sputu5pju21l-1 > li:before{content:"- "}.lst-kix_jpaysgvdrnw2-7 > li:before{content:"- "}ol.lst-kix_k3xb21291put-5{list-style-type:none}.lst-kix_jpaysgvdrnw2-5 > li:before{content:"- "}.lst-kix_i1ngeq9ml73k-1 > li:before{content:"" counter(lst-ctn-kix_i1ngeq9ml73k-1,lower-latin) ". "}.lst-kix_k3xb21291put-0 > li{counter-increment:lst-ctn-kix_k3xb21291put-0}ol.lst-kix_k3xb21291put-6{list-style-type:none}ol.lst-kix_k3xb21291put-3.start{counter-reset:lst-ctn-kix_k3xb21291put-3 0}ol.lst-kix_k3xb21291put-7{list-style-type:none}ol.lst-kix_k3xb21291put-8{list-style-type:none}.lst-kix_lrnabi51sw2p-5 > li{counter-increment:lst-ctn-kix_lrnabi51sw2p-5}ol.lst-kix_k3xb21291put-1{list-style-type:none}ol.lst-kix_k3xb21291put-2{list-style-type:none}ol.lst-kix_k3xb21291put-3{list-style-type:none}ol.lst-kix_k3xb21291put-4{list-style-type:none}ul.lst-kix_um1rr2y18kam-3{list-style-type:none}ul.lst-kix_jpaysgvdrnw2-8{list-style-type:none}ul.lst-kix_um1rr2y18kam-4{list-style-type:none}ul.lst-kix_um1rr2y18kam-1{list-style-type:none}ul.lst-kix_jpaysgvdrnw2-6{list-style-type:none}ul.lst-kix_um1rr2y18kam-2{list-style-type:none}ul.lst-kix_jpaysgvdrnw2-7{list-style-type:none}ul.lst-kix_um1rr2y18kam-7{list-style-type:none}ul.lst-kix_jpaysgvdrnw2-4{list-style-type:none}ul.lst-kix_um1rr2y18kam-8{list-style-type:none}ul.lst-kix_jpaysgvdrnw2-5{list-style-type:none}ul.lst-kix_um1rr2y18kam-5{list-style-type:none}ul.lst-kix_jpaysgvdrnw2-2{list-style-type:none}.lst-kix_i1ngeq9ml73k-7 > li{counter-increment:lst-ctn-kix_i1ngeq9ml73k-7}ul.lst-kix_um1rr2y18kam-6{list-style-type:none}ul.lst-kix_jpaysgvdrnw2-3{list-style-type:none}ul.lst-kix_jpaysgvdrnw2-0{list-style-type:none}ul.lst-kix_jpaysgvdrnw2-1{list-style-type:none}ol.lst-kix_lrnabi51sw2p-2.start{counter-reset:lst-ctn-kix_lrnabi51sw2p-2 0}ol.lst-kix_k3xb21291put-2.start{counter-reset:lst-ctn-kix_k3xb21291put-2 0}ol.lst-kix_i1ngeq9ml73k-2.start{counter-reset:lst-ctn-kix_i1ngeq9ml73k-2 0}ul.lst-kix_um1rr2y18kam-0{list-style-type:none}ol.lst-kix_lrnabi51sw2p-3.start{counter-reset:lst-ctn-kix_lrnabi51sw2p-3 0}ol.lst-kix_i1ngeq9ml73k-0.start{counter-reset:lst-ctn-kix_i1ngeq9ml73k-0 0}ol.lst-kix_k3xb21291put-4.start{counter-reset:lst-ctn-kix_k3xb21291put-4 0}.lst-kix_i1ngeq9ml73k-0 > li{counter-increment:lst-ctn-kix_i1ngeq9ml73k-0}.lst-kix_lrnabi51sw2p-2 > li{counter-increment:lst-ctn-kix_lrnabi51sw2p-2}ol.lst-kix_i1ngeq9ml73k-2{list-style-type:none}ol.lst-kix_i1ngeq9ml73k-1{list-style-type:none}ol.lst-kix_i1ngeq9ml73k-0{list-style-type:none}ol.lst-kix_i1ngeq9ml73k-8{list-style-type:none}ol.lst-kix_i1ngeq9ml73k-7{list-style-type:none}ol.lst-kix_i1ngeq9ml73k-6{list-style-type:none}ol.lst-kix_i1ngeq9ml73k-5{list-style-type:none}ol.lst-kix_i1ngeq9ml73k-4{list-style-type:none}ol.lst-kix_i1ngeq9ml73k-3{list-style-type:none}.lst-kix_i1ngeq9ml73k-8 > li:before{content:"" counter(lst-ctn-kix_i1ngeq9ml73k-8,lower-roman) ". "}.lst-kix_lrnabi51sw2p-0 > li{counter-increment:lst-ctn-kix_lrnabi51sw2p-0}ol.lst-kix_i1ngeq9ml73k-5.start{counter-reset:lst-ctn-kix_i1ngeq9ml73k-5 0}ul.lst-kix_e0nfih6q87yj-1{list-style-type:none}ul.lst-kix_e0nfih6q87yj-0{list-style-type:none}ul.lst-kix_e0nfih6q87yj-3{list-style-type:none}.lst-kix_lrnabi51sw2p-4 > li{counter-increment:lst-ctn-kix_lrnabi51sw2p-4}ul.lst-kix_e0nfih6q87yj-2{list-style-type:none}ul.lst-kix_e0nfih6q87yj-5{list-style-type:none}ul.lst-kix_e0nfih6q87yj-4{list-style-type:none}ul.lst-kix_e0nfih6q87yj-7{list-style-type:none}ul.lst-kix_e0nfih6q87yj-6{list-style-type:none}ul.lst-kix_e0nfih6q87yj-8{list-style-type:none}ol.lst-kix_k3xb21291put-5.start{counter-reset:lst-ctn-kix_k3xb21291put-5 0}ol.lst-kix_i1ngeq9ml73k-6.start{counter-reset:lst-ctn-kix_i1ngeq9ml73k-6 0}.lst-kix_i1ngeq9ml73k-2 > li{counter-increment:lst-ctn-kix_i1ngeq9ml73k-2}.lst-kix_k3xb21291put-8 > li{counter-increment:lst-ctn-kix_k3xb21291put-8}.lst-kix_lrnabi51sw2p-7 > li{counter-increment:lst-ctn-kix_lrnabi51sw2p-7}ol.lst-kix_k3xb21291put-8.start{counter-reset:lst-ctn-kix_k3xb21291put-8 0}.lst-kix_k3xb21291put-4 > li{counter-increment:lst-ctn-kix_k3xb21291put-4}.lst-kix_k3xb21291put-3 > li{counter-increment:lst-ctn-kix_k3xb21291put-3}.lst-kix_lrnabi51sw2p-8 > li{counter-increment:lst-ctn-kix_lrnabi51sw2p-8}ul.lst-kix_sputu5pju21l-4{list-style-type:none}ul.lst-kix_sputu5pju21l-3{list-style-type:none}ul.lst-kix_sputu5pju21l-6{list-style-type:none}.lst-kix_2ziulcxtjgb3-5 > li:before{content:"- "}.lst-kix_2ziulcxtjgb3-7 > li:before{content:"- "}ul.lst-kix_sputu5pju21l-5{list-style-type:none}ul.lst-kix_sputu5pju21l-8{list-style-type:none}ul.lst-kix_sputu5pju21l-7{list-style-type:none}.lst-kix_k3xb21291put-3 > li:before{content:"" counter(lst-ctn-kix_k3xb21291put-3,decimal) ". "}ul.lst-kix_sputu5pju21l-0{list-style-type:none}.lst-kix_k3xb21291put-1 > li:before{content:"" counter(lst-ctn-kix_k3xb21291put-1,lower-latin) ". "}.lst-kix_k3xb21291put-5 > li:before{content:"" counter(lst-ctn-kix_k3xb21291put-5,lower-roman) ". "}ul.lst-kix_sputu5pju21l-2{list-style-type:none}ul.lst-kix_sputu5pju21l-1{list-style-type:none}ol.lst-kix_lrnabi51sw2p-7.start{counter-reset:lst-ctn-kix_lrnabi51sw2p-7 0}ol.lst-kix_i1ngeq9ml73k-7.start{counter-reset:lst-ctn-kix_i1ngeq9ml73k-7 0}.lst-kix_e0nfih6q87yj-2 > li:before{content:"- "}.lst-kix_e0nfih6q87yj-0 > li:before{content:"- "}.lst-kix_lrnabi51sw2p-1 > li:before{content:"" counter(lst-ctn-kix_lrnabi51sw2p-1,lower-latin) ". "}.lst-kix_i1ngeq9ml73k-6 > li:before{content:"" counter(lst-ctn-kix_i1ngeq9ml73k-6,decimal) ". "}.lst-kix_jvm48z9p7qom-1 > li:before{content:"- "}.lst-kix_jpaysgvdrnw2-0 > li:before{content:"- "}.lst-kix_jpaysgvdrnw2-2 > li:before{content:"- "}.lst-kix_i1ngeq9ml73k-3 > li{counter-increment:lst-ctn-kix_i1ngeq9ml73k-3}.lst-kix_lrnabi51sw2p-3 > li:before{content:"" counter(lst-ctn-kix_lrnabi51sw2p-3,decimal) ". "}.lst-kix_lrnabi51sw2p-5 > li:before{content:"" counter(lst-ctn-kix_lrnabi51sw2p-5,lower-roman) ". "}.lst-kix_k3xb21291put-7 > li:before{content:"" counter(lst-ctn-kix_k3xb21291put-7,lower-latin) ". "}.lst-kix_i1ngeq9ml73k-4 > li:before{content:"" counter(lst-ctn-kix_i1ngeq9ml73k-4,lower-latin) ". "}.lst-kix_jvm48z9p7qom-3 > li:before{content:"- "}.lst-kix_e0nfih6q87yj-4 > li:before{content:"- "}.lst-kix_jpaysgvdrnw2-8 > li:before{content:"- "}.lst-kix_jpaysgvdrnw2-6 > li:before{content:"- "}.lst-kix_sputu5pju21l-0 > li:before{content:"- "}.lst-kix_e0nfih6q87yj-6 > li:before{content:"- "}ol.lst-kix_lrnabi51sw2p-8.start{counter-reset:lst-ctn-kix_lrnabi51sw2p-8 0}.lst-kix_i1ngeq9ml73k-2 > li:before{content:"" counter(lst-ctn-kix_i1ngeq9ml73k-2,lower-roman) ". "}.lst-kix_i1ngeq9ml73k-4 > li{counter-increment:lst-ctn-kix_i1ngeq9ml73k-4}.lst-kix_jpaysgvdrnw2-4 > li:before{content:"- "}.lst-kix_i1ngeq9ml73k-0 > li:before{content:"" counter(lst-ctn-kix_i1ngeq9ml73k-0,decimal) ". "}ol.lst-kix_i1ngeq9ml73k-8.start{counter-reset:lst-ctn-kix_i1ngeq9ml73k-8 0}.lst-kix_e0nfih6q87yj-8 > li:before{content:"- "}

Definition of Sample Space will be given on exam?If you want to learn more check out What is the trilogy of mind?

We also discuss several other topics like What is isoelcetronic mean?

Continuous Random Variables

  • Infinitely many outcomes in a probability experiment

Example: select a real number at random between 0 to 9We also discuss several other topics like What are the different types of financial statements?

        S = [0,9] is a continuous random variableIf you want to learn more check out What was California Channel Islands used for?

Questions:

        P(x=8) = 1/ = 0

        P(x>8) =

        P(x>8) =

  • Probability distribution curve for continuous random variables

R,xIf you want to learn more check out Why do we have fear?

Example: back to S = [0,9]

If you want to learn more check out How does structural unemployment function?

Area of rectangle = b x h

        1 = 9xh

        1/9 = h

Q: P (x>8) =

P(x>8)

= (1) x (1/9)

= 1/9

Q: P(x>8) = ?

        P(x>8)

        = (1) x 1/9

        = 1/9

Example: suppose exam 1 has a normal distribution with mean = M  = 74 and standard deviation = 0 = 11

Q: What is the probability of a randomly selected student with a grade above 80?

  • P(x>80) = ?

  • Probability
  1. P(A) = probability of event A

0<P(A)<1 → P(A) = 0 means impossible

                P(A) = 1 means certain

  1. P(s) = 1
  2. Complement rule

Definition: A0 = complement of event A

                = outcomes in S that are not in A

                = not A

Remember

P(A) + P(Ac) = 1 ← this is one that will be used in class

Equivalent equations

P(A) = 1 -P(AC)

P(AC) = 1 - P(A)

Example:

  1. A = {boy} → AC = {not not} = {girl}
  2. B = {even} → BC = {odd}
  3. C = {x>4} → CC = {X<4}
  4. D = {x<5} → DC = {X>5}
  5. E = {x=9} = EC = {x9}

Addition Rule

If A, B, are disjoint (mutually exclusive) events, then

P(A or B) = P(A) + P (B)

Definition:

A,B are disjoint events if they have no common outcome

Example:

  1. A = {boy}, B = {girl} → disjoint
  2. A = {green}, B = {yellow} → disjoint
  3. A = {student}, B = {workers} = not disjoint
  4. A = {odd}, B {x>4} → not disjoint
  5. A = {x<4}, B = {x>3} → not disjoint
  6. A = {grade A}, B = {pass} = not disjoint
  7. A = {x<4}, B = {x<3} = not disjoint
  8. A = {x<3}, B = {x>10} = disjoint

Rule number 5

Multiplication Rule

If A,B are independent events, then

P(A and B) = P(A) x P(B)

Definition:

A,B are independent events if the outcomes of one event will not change the probability of the other event

Example:

Pencil box: 8 green, 9 blue, 3 red

  • Will pick 2 pencils randomly

Q: P(1rst selection is green) = 8/20

Q: P(2nd selection is green) = ?

→ 2nd selection: Possible Outcomes

A: if you replace the first selection, then P(2nd selection is green) = 8/20

First selection and 2nd selection are independent events

B: if you don’t replace the first selection, then 2nd selection will be dependent on the outcome of the 1rst selection

  • If first selection is green, then the P(2nd selection is green) = 7/19
  • If the first selection is not green then P(2nd selection is green) = 8/19

1rst selection and second selection are not independent events (dependent events)

Example:

Suppose a probability model:

Outcome =         green                 blue                red                yellow

Probability           0.40                0.15                0.18                0.27

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