173/Omega/ff/fi/fl/ffi/ffl/dotlessi/dotlessj/grave/acute/caron/breve/macron/ring/cedilla/germandbls/ae/oe/oslash/AE/OE/Oslash/suppress/dieresis 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 endobj 17 0 obj Probability theory is also useful to engineers building systems that ha … >> The occurrence of R is difficult to predict — we have all been victims of wrong forecasts made by the Basic probability theory • Definition: Real-valued random variableX is a real-valued and measurable function defined on the sample space Ω, X: Ω→ ℜ – Each sample point ω ∈ Ω is associated with a real number X(ω) • Measurabilitymeans that all sets of type belong to the set of events , that is {X ≤ x} ∈ Let A be the set of hearts, and B be the set of even cards (counting 2, 4, 6, 8, 10 and Queen as even cards). /Length 524 10 0 obj xڽ�n���_1ȓ،x)�b줛f E�E2}�gh����D��k��sxHݭRl�D���ߨU��x��r�Vw��~4��ezu���I��� ��������FJ�_�":7eU�{�Qyħ��^��C�/�+a�WZ��ٲz������_��$�ziAf��R �^�����e b��Ս�$ ήnTj��I�N3*ʏ[$�?�[5yq��q�wx�l�D�)��`�)H�$�6�ϕ��MG��� ?��#�ж���d�{p†�H �3~m �;$*�rZz�7 �^vem��W7 l�9W��3h��h��2G� �8�Y�}W�bk�k8G�(�ϔ�%�/�ᴷ~�ш��)�����v���l;����_�谸^��Ȩw�>�K�4L"���Gd�px)�{U�T�.=ut{�٪n��0�D]#�QL�}���Kc�Ȉ&�Y�,���_t|�b-4ߜ� �7%�_�*�-6~��xq̤�]�/��?�#�����j�^�Lq�i��!U��'>����u�:�[�x+����f��Y� ��T�K�o]0x���~;����+�4;�JٷӳBmv�%'�n���[�~@��Fҩg�i,���k[4����[B5L����5�da=���%Ht��;�H��E���-/8�8I��G�4�kH����9�])�o}>X?�������s�6�Ǜ�}ʛ�9(% � �8l@ J?�_6��u��I;�#$��Wz̘�z�u�KSك��N�jgɨ��ix�8�{�~�D�t��u��8���u]\ػ�f�1K��U*��(z���@�D#�7L��~�v���&�x� ���6s)�p�z8}�s�X_��&��OD(&.��O��� =?����2Y�D'�� /F1 10 0 R }j�ԩS�:�C�B@n���r绰-& دm����CUn}�����*4]��C'�]�>7�&--���p���(�Q���[��bvߗ!��ćT2�V��}6 ��äU �0�{�u�8Z�;fr���w6�U��w�vw�(���#@�K(�� ��T��l���i�gJ10P��3� p1W\,V��Ā� ����*�5�wʎ��?K穃��{^�!�6'ے��t��]�6� ��fc�+�B�2��(�I9���djlX3��{#*��ϢI�$-7������l�u����58=��q}_q%�H���f�\�9^���|����a� W!��f��� ���8X9v {! /Subtype/Type1 277.8 500 555.6 444.4 555.6 444.4 305.6 500 555.6 277.8 305.6 527.8 277.8 833.3 555.6 << << Sign in Register; Hide. 500 500 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 625 833.3 /Type/Font 306.7 511.1 511.1 511.1 511.1 511.1 511.1 511.1 511.1 511.1 511.1 511.1 306.7 306.7 (ii) (A B) is an event, that occurs only when each one of 'A' and 'B' occur (A B) means ( A and B). Tutorial 3: Probability Theory, Random Variables and Distributions 2 Task 1: Consider a standard pack of 52 playing cards. endobj /BaseFont/TFISVD+CMSL10 750 708.3 722.2 763.9 680.6 652.8 784.7 750 361.1 513.9 777.8 625 916.7 750 777.8 /FontDescriptor 22 0 R 741.7 712.5 851.4 813.9 405.6 566.7 843 683.3 988.9 813.9 844.4 741.7 844.4 800 611.1 What is P(A)? The probability of random variable x is P(x), called probability mass… 30 0 obj /Type/Font 777.8 694.4 666.7 750 722.2 777.8 722.2 777.8 0 0 722.2 583.3 555.6 555.6 833.3 833.3 525 525 525 525 525 525 525 525 525 525 525 525 525 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 /Filter[/FlateDecode] >> 762.8 642 790.6 759.3 613.2 584.4 682.8 583.3 944.4 828.5 580.6 682.6 388.9 388.9 /FontDescriptor 47 0 R /Type/Font endobj /Font 37 0 R 532.2 767.8 560.6 561.7 490.6 591.1 1182.2 591.1 591.1 591.1 0 0 0 0 0 0 0 0 0 0 >> 277.8 305.6 500 500 500 500 500 750 444.4 500 722.2 777.8 500 902.8 1013.9 777.8 << /LastChar 196 >> /F6 26 0 R 575 1041.7 1169.4 894.4 319.4 575] /Differences[0/Gamma/Delta/Theta/Lambda/Xi/Pi/Sigma/Upsilon/Phi/Psi/Omega/ff/fi/fl/ffi/ffl/dotlessi/dotlessj/grave/acute/caron/breve/macron/ring/cedilla/germandbls/ae/oe/oslash/AE/OE/Oslash/suppress/exclam/quotedblright/numbersign/sterling/percent/ampersand/quoteright/parenleft/parenright/asterisk/plus/comma/hyphen/period/slash/zero/one/two/three/four/five/six/seven/eight/nine/colon/semicolon/exclamdown/equal/questiondown/question/at/A/B/C/D/E/F/G/H/I/J/K/L/M/N/O/P/Q/R/S/T/U/V/W/X/Y/Z/bracketleft/quotedblleft/bracketright/circumflex/dotaccent/quoteleft/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/endash/emdash/hungarumlaut/tilde/dieresis/Gamma/Delta/Theta/Lambda/Xi/Pi/Sigma/Upsilon/Phi/Psi/Omega/ff/fi/fl/ffi/ffl/dotlessi/dotlessj/grave/acute/caron/breve/macron/ring/cedilla/germandbls/ae/oe/oslash/AE/OE/Oslash/suppress/Gamma/Delta/Theta/Lambda/Xi/Pi/Sigma/Upsilon/Phi/Psi << Discrete random variable is a variable that can be any value in a set (sample space), which has a finite number of values. %PDF-1.2 48 0 obj Tutorial on probability theory A.1 Random events Probability theory is fundamental to much of our discussion in this book. I have written this brief tutorial with the specific aim of introducing the reader to … /Subtype/Type1 Probability. /Name/F6 255/dieresis] 812.5 875 562.5 1018.5 1143.5 875 312.5 562.5] 20 0 obj endobj /Name/F7 /LastChar 196 16 0 obj endstream >> >> /Encoding 7 0 R >> 460 511.1 306.7 306.7 460 255.6 817.8 562.2 511.1 511.1 460 421.7 408.9 332.2 536.7 endobj >> /Differences[33/exclam/quotedblright/numbersign/dollar/percent/ampersand/quoteright/parenleft/parenright/asterisk/plus/comma/hyphen/period/slash/zero/one/two/three/four/five/six/seven/eight/nine/colon/semicolon/exclamdown/equal/questiondown/question/at/A/B/C/D/E/F/G/H/I/J/K/L/M/N/O/P/Q/R/S/T/U/V/W/X/Y/Z/bracketleft/quotedblleft/bracketright/circumflex/dotaccent/quoteleft/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/endash/emdash/hungarumlaut/tilde/dieresis/Gamma/Delta/Theta/Lambda/Xi/Pi/Sigma/Upsilon/Phi/Psi/Omega/ff/fi/fl/ffi/ffl/dotlessi/dotlessj/grave/acute/caron/breve/macron/ring/cedilla/germandbls/ae/oe/oslash/AE/OE/Oslash/suppress/Gamma/Delta/Theta/Lambda/Xi/Pi/Sigma/Upsilon/Phi/Psi What is P(B)? 32 0 obj Economics (101) Academic year. ... (From set – theory). >> << 666.7 666.7 666.7 666.7 611.1 611.1 444.4 444.4 444.4 444.4 500 500 388.9 388.9 277.8 /F1 10 0 R stream 42 0 obj 6 0 obj