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INTRO

UNIT 4 PROBABILITY
GLOSSARY
Discrete Probability Distributions
Random variable
Probability distribution
Discrete random variable
Continuous random variable
Variance
Standard Deviation
Usual Values
Minimum Usual values
Normal Distribution

_x000D_&1#&"Calibri"&10&K000000 INTERNAL - RESTRICTED

SUMMARY

DISCRETE RANDOM VARIABLES

_x000D_&1#&"Calibri"&10&K000000 INTERNAL - RESTRICTED

PROJECT 4.1

DISCRETE RANDOM VARIABLES
Day Occupied_Rooms
1 3
2 7
3 6
4 2
5 4
6 8
7 0
8 4
9 8
10 3
11 4
12 5
13 8
14 4
15 4
16 4
17 10
18 10
19 7
20 6
21 7
22 8
23 3
24 7
25 2
26 4
27 7
28 2
29 5
30 3
31 4
32 0
33 1
34 4
35 7
36 5
37 5
38 6
39 3
40 6
41 3
42 1
43 4
44 6
45 6
46 5
47 10
48 6
49 7
50 10
51 2
52 3
53 9
54 3
55 5
56 7
57 7
58 9
59 8
60 7
61 3
62 7
63 6
64 2
65 8
66 7
67 5
68 5
69 2
70 5
71 6
72 3
73 7
74 3
75 1
76 7
77 4
78 5
79 3
80 2
81 8
82 4
83 8
84 7
85 4
86 3
87 3
88 2
89 9
90 5
91 7
92 2
93 5
94 7
95 4
96 7
97 3
98 2
99 6
100 4
101 6
102 1
103 6
104 10
105 5
106 5
107 5
108 1
109 6
110 2
111 4
112 8
113 3
114 6
115 7
116 6
117 2
118 4
119 9
120 1
121 4
122 4
123 5
124 7
125 8
126 4
127 7
128 6
129 6
130 4
131 3
132 3
133 3
134 6
135 7
136 6
137 4
138 9
139 8
140 4
141 3
142 5
143 8
144 6
145 6
146 5
147 6
148 8
149 4
150 5
151 6
152 6
153 2
154 1
155 3
156 5
157 6
158 4
159 8
160 5
161 5
162 5
163 5
164 6
165 6
166 3
167 8
168 3
169 5
170 4
171 3
172 5
173 3
174 5
175 6
176 8
177 6
178 4
179 4
180 5
181 5
182 8
183 8
184 4
185 4
186 0
187 4
188 3
189 4
190 6
191 5
192 5
193 5
194 5
195 5
196 0
197 4
198 5
199 4
200 5
201 6
202 4
203 10
204 6
205 5
206 5
207 5
208 3
209 5
210 6
211 6
212 6
213 4
214 2
215 4
216 8
217 7
218 6
219 3
220 5
221 2
222 4
223 4
224 4
225 7
226 2
227 3
228 2
229 2
230 5
231 2
232 7
233 4
234 5
235 6
236 4
237 7
238 5
239 6
240 5
241 6
242 6
243 6
244 3
245 6
246 4
247 6
248 0
249 2
250 6
251 9
252 7
253 4
254 1
255 7
256 5
257 6
258 5
259 5
260 11
261 5
262 5
263 5
264 4
265 7
266 4
267 6
268 6
269 8
270 6
271 2
272 2
273 8
274 4
275 2
276 4
277 8
278 2
279 3
280 4
281 2
282 3
283 2
284 4
285 4
286 4
287 2
288 8
289 2
290 6
291 3
292 6
293 7
294 3
295 1
296 6
297 9
298 6
299 5
300 7
301 7
302 3
303 4
304 6
305 5
306 8
307 4
308 7
309 6
310 5
311 7
312 6
313 3
314 6
315 8
316 5
317 4
318 4
319 5
320 6
321 3
322 2
323 4
324 2
325 6
326 4
327 1
328 4
329 5
330 6
331 5
332 9
333 4
334 5
335 5
336 4
337 5
338 6
339 8
340 2
341 4
342 4
343 7
344 4
345 1
346 5
347 5
348 5
349 3
350 9
351 4
352 5
353 3
354 3
355 2
356 4
357 3
358 9
359 1
360 3
361 4
362 6
363 4
364 6
365 3
366 5
367 9
368 3
369 6
370 5
371 0
372 4
373 7
374 5
375 2
376 6
377 4
378 6
379 6
380 3
381 7
382 3
383 2
384 3
385 4
386 5
387 3
388 7
389 6
390 4
391 7
392 7
393 5
394 5
395 1
396 4
397 4
398 6
399 5
400 6
401 8
402 4
403 4
404 2
405 5
406 7
407 1
408 4
409 5
410 7
411 6
412 6
413 5
414 6
415 7
416 1
417 7
418 5
419 4
420 0
421 2
422 9
423 4
424 3
425 4
426 3
427 5
428 8
429 4
430 5
431 3
432 8
433 5
434 3
435 7
436 8
437 5
438 2
439 9
440 6
441 7
442 4
443 4
444 5
445 7
446 5
447 2
448 6
449 8
450 5
451 5
452 2
453 2
454 4
455 4
456 5
457 5
458 8
459 5
460 7
461 5
462 8
463 1
464 4
465 7
466 5
467 7
468 6
469 7
470 6
471 6
472 8
473 7
474 7
475 5
476 4
477 4
478 7
479 0
480 2
481 3
482 4
483 0
484 8
485 6
486 9
487 7
488 7
489 10
490 4
491 2
492 5
493 3
494 4
495 3
496 6
497 6
498 5
499 6
500 5
501 7
502 5
503 4
504 7
505 8
506 8
507 3
508 4
509 1
510 4
511 6
512 5
513 9
514 4
515 3
516 6
517 5
518 6
519 6
520 6
521 1
522 3
523 4
524 4
525 4
526 6
527 6
528 3
529 6
530 6
531 6
532 2
533 6
534 5
535 7
536 9
537 8
538 5
539 5
540 6
541 3
542 2
543 4
544 8
545 4
546 8
547 0
548 2
549 5
550 7
551 5
552 5
553 5
554 1
555 7
556 4
557 7
558 5
559 7
560 6
561 5
562 5
563 2
564 5
565 9
566 8
567 3
568 6
569 6
570 7
571 5
572 5
573 8
574 5
575 8
576 7
577 4
578 5
579 9
580 5
581 3
582 2
583 7
584 5
585 3
586 6
587 5
588 2
589 6
590 8
591 10
592 5
593 5
594 8
595 5
596 6
597 4
598 2
599 7
600 2
601 7
602 3
603 6
604 4
605 7
606 6
607 9
608 3
609 6
610 5
611 6
612 8
613 6
614 3
615 6
616 4
617 4
618 7
619 4
620 4
621 5
622 7
623 6
624 5
625 4
626 3
627 3
628 4
629 5
630 9
631 4
632 4
633 1
634 6
635 2
636 3
637 7
638 1
639 5
640 7
641 8
642 3
643 4
644 9
645 5
646 3
647 3
648 3
649 4
650 7
651 7
652 3
653 5
654 4
655 7
656 5
657 6
658 5
659 0
660 5
661 2
662 7
663 4
664 4
665 5
666 6
667 5
668 8
669 8
670 9
671 5
672 2
673 8
674 4
675 5
676 6
677 2
678 8
679 7
680 6
681 7
682 6
683 5
684 4
685 3
686 6
687 6
688 7
689 5
690 3
691 2
692 5
693 5
694 5
695 2
696 7
697 7
698 3
699 7
700 7
701 5
702 3
703 8
704 6
705 4
706 7
707 8
708 4
709 6
710 9
711 3
712 4
713 4
714 5
715 5
716 6
717 3
718 4
719 6
720 5
721 7
722 6
723 7
724 3
725 4
726 9
727 6
728 7
729 6
730 6
731 5
732 13
733 4
734 5
735 0
736 7
737 4
738 5
739 4
740 5
741 4
742 5
743 5
744 5
745 5
746 8
747 7
748 7
749 3
750 8
751 7
752 4
753 8
754 4
755 1
756 7
757 5
758 7
759 3
760 2
761 8
762 2
763 2
764 1
765 0
766 3
767 0
768 5
769 0
770 3
771 10
772 6
773 5
774 2
775 4
776 5
777 2
778 5
779 8
780 4
781 5
782 1
783 2
784 7
785 4
786 3
787 4
788 5
789 3
790 5
791 2
792 7
793 3
794 8
795 5
796 3
797 7
798 2
799 4
800 5
801 5
802 1
803 3
804 5
805 2
806 8
807 6
808 4
809 5
810 9
811 7
812 6
813 2
814 8
815 7
816 5
817 4
818 5
819 2
820 4
821 7
822 1
823 4
824 5
825 5
826 3
827 3
828 7
829 2
830 7
831 4
832 7
833 4
834 3
835 7
836 5
837 8
838 7
839 5
840 4
841 5
842 5
843 3
844 7
845 4
846 4
847 4
848 5
849 4
850 5
851 11
852 5
853 4
854 1
855 5
856 3
857 4
858 5
859 1
860 5
861 6
862 2
863 4
864 1
865 8
866 6
867 5
868 5
869 7
870 5
871 6
872 8
873 4
874 3
875 3
876 8
877 5
878 4
879 7
880 7
881 4
882 3
883 2
884 1
885 4
886 3
887 9
888 5
889 1
890 8
891 5
892 6
893 6
894 6
895 6
896 6
897 3
898 6
899 7
900 5
901 6
902 6
903 9
904 4
905 4
906 5
907 5
908 0
909 4
910 6
911 5
912 3
913 4
914 4
915 3
916 4
917 4
918 7
919 7
920 7
921 6
922 4
923 7
924 4
925 5
926 8
927 5
928 6
929 2
930 6
931 3
932 7
933 5
934 0
935 4
936 5
937 6
938 6
939 4
940 7
941 0
942 4
943 3
944 2
945 7
946 7
947 3
948 7
949 5
950 4
951 4
952 3
953 6
954 6
955 6
956 1
957 6
958 6
959 4
960 5
961 1
962 2
963 4
964 4
965 6
966 3
967 4
968 4
969 6
970 8
971 9
972 2
973 5
974 3
975 5
976 6
977 5
978 5
979 8
980 7
981 4
982 5
983 7
984 6
985 4
986 1
987 3
988 5
989 1
990 5
991 4
992 7
993 2
994 1
995 4
996 6
997 7
998 3
999 6
1000 3

_x000D_&1#&"Calibri"&10&K000000 INTERNAL - RESTRICTED

PROJECT 4.2

CONTINUOUS RANDOM VARIABLES
Customer_ID Restaurant Stay_Time_Minutes
1 58.6
2 71
3 38.4
4 50
5 58.5
6 92.2
7 80.9
8 56.9
9 71.5
10 63.1
11 44.4
12 47.6
13 44.2
14 58.7
15 62.4
16 33.2
17 76
18 60.6
19 57.5
20 55.1
21 83.8
22 57.2
23 57.3
24 70.8
25 60
26 71.7
27 61.3
28 61
29 78
30 59.1
31 46.5
32 41.1
33 60.8
34 45.5
35 71.2
36 64.2
37 55.3
38 50.2
39 58.9
40 68.9
41 72.9
42 42.1
43 88.5
44 50.3
45 42.3
46 83.3
47 78.2
48 74
49 49.9
50 76
51 58.4
52 39.1
53 49.9
54 41.1
55 73.5
56 77.6
57 44.4
58 57.7
59 65.9
60 42.5
61 74.1
62 44.9
63 39.1
64 47.3
65 54.4
66 47.1
67 78.1
68 60
69 38.6
70 65.1
71 38.5
72 83
73 42
74 53.3
75 62.9
76 48.3
77 45.2
78 63.8
79 36.6
80 75.6
81 40.6
82 41.2
83 57.8
84 26.8
85 59.7
86 49.1
87 65
88 58.4
89 73.5
90 46.5
91 71.9
92 60
93 52.2
94 63.2
95 48.4
96 51.1
97 51.9
98 62.7
99 58.2
100 28
101 81.5
102 85.9
103 50.4
104 72.5
105 68.3
106 53.6
107 56.9
108 76
109 35.9
110 72.2
111 78.7
112 50.4
113 82.1
114 71.9
115 76.4
116 58.6
117 44.5
118 54.4
119 26.1
120 47.5
121 70
122 47.2
123 65.7
124 90.4
125 51.9
126 65
127 36.8
128 74.1
129 74
130 50.2
131 45.5
132 53.4
133 41.2
134 68.2
135 75.8
136 61.8
137 32.9
138 83.9
139 67.2
140 63.5
141 35.8
142 58.3
143 60.7
144 61.6
145 68.7
146 47.3
147 52.7
148 48.6
149 56.6
150 32.6
151 74.3
152 67.1
153 71.3
154 57.6
155 64.3
156 52.5
157 83.6
158 41.2
159 39.5
160 58
161 62.5
162 95.2
163 75.7
164 68.1
165 46.8
166 45.3
167 45.2
168 71.6
169 74
170 73.2
171 45.7
172 38.4
173 61.2
174 67
175 63
176 71.5
177 72.3
178 78.8
179 71.7
180 35.7
181 49.7
182 56.6
183 87.6
184 49.5
185 55.3
186 56.6
187 70.5
188 55.2
189 64.2
190 39.1
191 61.4
192 77.6
193 68.5
194 56.5
195 72.9
196 72.6
197 66.1
198 70.3
199 75.7
200 49.1
201 50.9
202 69.7
203 85.6
204 58.3
205 44.5
206 78.4
207 55.2
208 53.9
209 24.3
210 58
211 68.9
212 44.8
213 73.2
214 44.2
215 50.4
216 45.1
217 45.9
218 37
219 54.1
220 53
221 54.6
222 62
223 33.9
224 66.3
225 67.8
226 56.6
227 67.7
228 57.9
229 86.3
230 75.2
231 71.4
232 38.8
233 59.4
234 69.8
235 73.6
236 58.6
237 89.6
238 66.5
239 50.5
240 49.9
241 67.8
242 72.1
243 68.5
244 57.4
245 76.5
246 38
247 51.1
248 62.4
249 72.8
250 67
251 44.3
252 76.7
253 82.9
254 86.8
255 65.2
256 92.3
257 69.8
258 65.6
259 61.1
260 49.5
261 55.8
262 61.2
263 54.5
264 60.3
265 27.2
266 75.1
267 34.3
268 62.9
269 61.8
270 58.4
271 50.8
272 72.9
273 68.4
274 71.9
275 50
276 76.2
277 44.3
278 64
279 42.8
280 71.1
281 45.8
282 76
283 33.6
284 40.3
285 56.4
286 61.5
287 80.3
288 62
289 69.2
290 44.3
291 54.5
292 46.4
293 56.6
294 60.9
295 49.1
296 66.6
297 69.7
298 30.2
299 40.2
300 47.1
301 50.6
302 59.1
303 61.1
304 42.6
305 54.5
306 48.7
307 75.8
308 55.7
309 48.7
310 69.4
311 50.1
312 33.2
313 53.4
314 48.5
315 40.9
316 63
317 61.7
318 62.1
319 93.6
320 52.2
321 23.4
322 50.4
323 51.5
324 65.4
325 73.2
326 62.3
327 28.8
328 53.1
329 55.3
330 38.8
331 70.6
332 52.9
333 45.4
334 57.4
335 44.5
336 60.2
337 70.7
338 56
339 43.1
340 39.2
341 62.6
342 47.1
343 54.8
344 47.7
345 52.8
346 75.3
347 48.6
348 58.9
349 43.7
350 52
351 53.7
352 53.5
353 57
354 43.4
355 55.1
356 81.2
357 46.6
358 71.5
359 91.7
360 56.4
361 80.3
362 40.5
363 78.6
364 63
365 78.4
366 46.6
367 62.4
368 42.8
369 55
370 34.1
371 58.8
372 47.1
373 49.5
374 72.4
375 24.4
376 45.8
377 45.9
378 65.6
379 77.1
380 56.2
381 52.4
382 76.9
383 66.4
384 59.8
385 76.8
386 61.4
387 50.8
388 78.8
389 65
390 50
391 44.1
392 58.3
393 64
394 55.5
395 51.6
396 60.8
397 85.8
398 65.4
399 68.1
400 58.6
401 66.4
402 60.3
403 70.8
404 57.4
405 69
406 61.5
407 71.3
408 40.9
409 54.7
410 88.7
411 86.2
412 99
413 67.3
414 55.9
415 73.1
416 52.4
417 75.7
418 45
419 71.6
420 35.1
421 60.5
422 86.9
423 32.8
424 65.9
425 52.6
426 84.1
427 32.3
428 39.4
429 95.5
430 53.2
431 57.9
432 53.8
433 69.1
434 54.1
435 56.4
436 45.7
437 62.9
438 67
439 77
440 68.6
441 65.3
442 58.9
443 80.6
444 40.5
445 51.7
446 52.8
447 47.7
448 63.5
449 56
450 69.2
451 43.4
452 61.5
453 81.1
454 46.3
455 51.9
456 64
457 49.4
458 49.8
459 51.4
460 55.7
461 47.4
462 45.2
463 45.1
464 56
465 86.7
466 60.5
467 61.2
468 30.5
469 71.5
470 67.1
471 59.7
472 45
473 52
474 58.6
475 74.7
476 64.1
477 27.3
478 35.9
479 51.1
480 75.6
481 34.3
482 58.5
483 53.9
484 55.7
485 74
486 76.4
487 61.6
488 32.9
489 73.9
490 77.1
491 46.9
492 46.6
493 81.2
494 46.5
495 75.3
496 65.4
497 71.7
498 60.7
499 71
500 33.6
501 45.6
502 46.2
503 50.3
504 58.6
505 66.7
506 69.2
507 37.7
508 61.8
509 50.9
510 45.6
511 80.6
512 54.7
513 61.9
514 47.1
515 68.5
516 52
517 49
518 49.1
519 71.6
520 83.4
521 69.5
522 34.5
523 54.4
524 96.6
525 65.5
526 54.5
527 62.7
528 41.7
529 56.9
530 49.3
531 54.9
532 68.2
533 75.1
534 45.3
535 39
536 65.9
537 64.3
538 68.1
539 43.5
540 71
541 51
542 73
543 67.4
544 61
545 47.2
546 43.2
547 49.5
548 45.1
549 63.4
550 56.2
551 62.4
552 57.5
553 61.1
554 60
555 58.8
556 63.7
557 41
558 46.6
559 49.9
560 22.2
561 83.1
562 49
563 61.1
564 53
565 48.4
566 44.2
567 66.9
568 66
569 61.3
570 76
571 68.6
572 53.1
573 60.8
574 55.1
575 87.5
576 62.3
577 28.8
578 90.7
579 39.4
580 89.3
581 60.6
582 61.2
583 65.3
584 57.7
585 69.1
586 55.3
587 39.6
588 65.8
589 64.1
590 60.7
591 77.4
592 66.9
593 67.9
594 62.7
595 46.9
596 51.4
597 62
598 50.2
599 67.6
600 69.4
601 69.6
602 80.4
603 47.8
604 30.6
605 61
606 75.1
607 50.2
608 57
609 61
610 57.1
611 67.6
612 61.5
613 39.7
614 86.7
615 70.4
616 61.2
617 62.2
618 45.4
619 42.8
620 47.2
621 71.2
622 86.2
623 74.1
624 56.4
625 69.8
626 81.4
627 49.9
628 77.4
629 71.7
630 48
631 69.1
632 93
633 56.6
634 75.5
635 56.3
636 74.2
637 49.6
638 54.5
639 65.4
640 79.4
641 80.7
642 54.9
643 75
644 72.5
645 85.1
646 54.7
647 51.3
648 80.2
649 43.9
650 52.5
651 49.1
652 66
653 49.3
654 48.7
655 68.2
656 84.9
657 70.2
658 69.9
659 59.1
660 65.5
661 56
662 53.7
663 41.7
664 56
665 59.1
666 74.3
667 62.7
668 57.5
669 38.4
670 33.8
671 59.9
672 54.5
673 61.5
674 50.3
675 65.1
676 44.9
677 75.8
678 76.8
679 12.2
680 57
681 38.5
682 58.6
683 36.7
684 24
685 59.9
686 64.8
687 61.1
688 87.9
689 70.6
690 53.7
691 44.9
692 51.6
693 52.4
694 66.6
695 53.6
696 63.6
697 66
698 61.9
699 53.3
700 66
701 76.1
702 28.6
703 87
704 46.8
705 38.3
706 71.5
707 63.6
708 61.9
709 68.6
710 69.3
711 67.5
712 60.8
713 13.5
714 69.7
715 68
716 50.1
717 50.9
718 67
719 51.8
720 39.1
721 38.9
722 64.2
723 63.2
724 79.3
725 45.5
726 73.6
727 59
728 43.6
729 63.8
730 67.7
731 84
732 43.4
733 35.1
734 73.3
735 51.5
736 61.9
737 54.8
738 61.5
739 40.5
740 38.2
741 54.6
742 55.6
743 44.4
744 60.7
745 66.3
746 64.1
747 56.3
748 46.5
749 65.9
750 55.3
751 39.4
752 46
753 52.4
754 51.7
755 17.8
756 66.5
757 61.5
758 51.4
759 63.3
760 60.5
761 54.7
762 55.2
763 52.7
764 64.5
765 57.2
766 70.5
767 57.3
768 52.7
769 67.2
770 57.7
771 51.6
772 46.5
773 75.8
774 70.9
775 61.8
776 47.1
777 93.9
778 82.9
779 77.1
780 66.3
781 56
782 70.8
783 64.3
784 64.6
785 53.5
786 59.9
787 50
788 72.4
789 56.8
790 93.2
791 52
792 62.5
793 86.4
794 47
795 77.7
796 45.2
797 61.4
798 58.8
799 57.4
800 82.5
801 80.1
802 70.8
803 58.8
804 35
805 70.5
806 59.6
807 48.7
808 63.6
809 63.3
810 57.5
811 66.6
812 95.2
813 55
814 76.7
815 94.7
816 67.1
817 64
818 76.3
819 61.5
820 66.3
821 40.1
822 59
823 81.6
824 61.4
825 89.9
826 61.4
827 72.5
828 48.4
829 57.4
830 54.7
831 61.6
832 70.5
833 52
834 42.7
835 60.9
836 70.6
837 83.2
838 42.2
839 32.4
840 52.3
841 80.1
842 42.6
843 51.9
844 84
845 55.8
846 59.6
847 63.1
848 71.7
849 57.8
850 32.5
851 58.3
852 65.4
853 17.4
854 78.9
855 56.9
856 35.1
857 53.1
858 86.1
859 71.9
860 62.4
861 58.4
862 27.1
863 59.3
864 75
865 47.1
866 68.6
867 48.3
868 69
869 40.1
870 65.6
871 39.6
872 36.5
873 52.9
874 55.4
875 61.7
876 45.5
877 52.9
878 59
879 77.1
880 76.7
881 61.6
882 82.1
883 58.9
884 93.2
885 81.1
886 53.4
887 50.6
888 56.3
889 76.3
890 48.1
891 68.9
892 64.5
893 79.9
894 45.6
895 54.9
896 48
897 77.1
898 91.4
899 70.2
900 73.4
901 49.9
902 79
903 46.9
904 60.3
905 50.1
906 55.4
907 68.4
908 80.7
909 43.1
910 48.3
911 63.5
912 59.1
913 64.8
914 49.4
915 51.6
916 44.7
917 66.8
918 51.7
919 69.8
920 70.6
921 63.4
922 78.4
923 71.2
924 80.1
925 48.5
926 74.9
927 64.9
928 58.4
929 86.8
930 49.1
931 60.4
932 62.9
933 56.7
934 72.2
935 84.1
936 76.4
937 43
938 48.1
939 74.4
940 46.1
941 58.6
942 44.1
943 29.5
944 33
945 49.6
946 69.8
947 62.2
948 64.2
949 66.3
950 58.9
951 77
952 62.1
953 62.4
954 84.6
955 55.3
956 63.8
957 63.8
958 80.3
959 77.4
960 43.5
961 47
962 61.3
963 61.8
964 88.6
965 69.9
966 59.9
967 69.8
968 39.2
969 65.7
970 69.2
971 28.8
972 46.3
973 57.7
974 45.6
975 58.8
976 59.5
977 38.8
978 60
979 67.5
980 82.4
981 37.8
982 44.8
983 67.9
984 89.4
985 52.3
986 62.2
987 52.5
988 27.9
989 45.1
990 71.9
991 57
992 53.7
993 57.6
994 52.8
995 35.9
996 40.9
997 55.4
998 54.1
999 35.8
1000 69.5

_x000D_&1#&"Calibri"&10&K000000 INTERNAL - RESTRICTED

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