Problem solving tasktaskProblem solvingtaskProblem solving taskContiguous U.S. Average...

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Problem solving tasktaskProblem solvingtaskProblem solving taskContiguous U.S.	 Average Temperature		 Units: Degrees Fahrenheit			 Base Period: 1901-2000			 Missing: -99			 Date	Value		 189901	29.68		 189902	25.5		 189903	37.63		 189904	50.61		 189905	59.9		 189906	68.65		 189907	73.08		 189908	71.74		 189909	64.8		 189910	53.98		 189911	44.92		 189912	31.62		 190001	34.11		 190002	30.76		 190003	41.27		 190004	51.6		 190005	61.74		 190006	70.3		 190007	73.13		 190008	72.86		 190009	65.14		 190010	56.35		 190011	41.54		 190012	34.48		 190101	31.62		 190102	29.86		 190103	40.71		 190104	49.39		 190105	61.18		 190106	68.43		 190107	76.24		 190108	73.2		 190109	63.25		 190110	55.45		 190111	41.68		 190112	31.48		 190201	30.06		 190202	31.46		 190203	41.58		 190204	50.85		 190205	61.99		 190206	68.04		 190207	72.05		 190208	71.37		 190209	62.76		 190210	54.43		 190211	43.68		 190212	30.79		 190301	30.88		 190302	28.42		 190303	42.21		 190304	50.22		 190305	59.54		 190306	65.89		 190307	71.92		 190308	70.97		 190309	62.73		 190310	53.94		 190311	40.23		 190312	30.54		 190401	27.55		 190402	31.59		 190403	41.76		 190404	49.46		 190405	60.13		 190406	67.26		 190407	71.35		 190408	70.72		 190409	64.96		 190410	53.92		 190411	43.14		 190412	32.02		 190501	27.1		 190502	26.94		 190503	45.12		 190504	50.49		 190505	59.14		 190506	68		 190507	71.98		 190508	72.37		 190509	65.95		 190510	51.64		 190511	42.24		 190512	30.99		 190601	32.88		 190602	33.69		 190603	36.1		 190604	52.72		 190605	59.58		 190606	67.32		 190607	72.36		 190608	71.85		 190609	66.25		 190610	52.54		 190611	40.44		 190612	34.97		 190701	30.69		 190702	35.46		 190703	45.7		 190704	47.53		 190705	55.89		 190706	65.7		 190707	72.52		 190708	70.79		 190709	64.22		 190710	53.78		 190711	40.82		 190712	34.7		 190801	32.45		 190802	33.01		 190803	43.92		 190804	52.75		 190805	58.82		 190806	66.92		 190807	73.18		 190808	70.68		 190809	65.59		 190810	51.76		 190811	42.53		 190812	33.31		 190901	32.31		 190902	35.02		 190903	40.35		 190904	48.96		 190905	58.14		 190906	68.94		 190907	72.63		 190908	72.93		 190909	64.4		 190910	52.88		 190911	45.03		 190912	25.61		 191001	29.61		 191002	29.3		 191003	49.44		 191004	53.62		 191005	59.22		 191006	68.29		 191007	74.12		 191008	71.11		 191009	65.68		 191010	55.62		 191011	41.13		 191012	31.93		 191101	32.9		 191102	33.66		 191103	44.02		 191104	50		 191105	61.21		 191106	70.75		 191107	72.68		 191108	70.9		 191109	66.09		 191110	52.66		 191111	37.27		 191112	32.2		 191201	24.76		 191202	31.08		 191203	35.76		 191204	50.58		 191205	60.48		 191206	66.7		 191207	72.25		 191208	70.12		 191209	62.73		 191210	53.17		 191211	42.21		 191212	32.95		 191301	30.47		 191302	29.5		 191303	38.71		 191304	51.39		 191305	60.13		 191306	68.22		 191307	73		 191308	73.36		 191309	63.64		 191310	51.64		 191311	45.12		 191312	33.33		 191401	34.5		 191402	29.52		 191403	40.75		 191404	51.04		 191405	61.14		 191406	69.35		 191407	74.08		 191408	71.69		 191409	64.58		 191410	55.24		 191411	43.41		 191412	26.78		 191501	28.44		 191502	35.94		 191503	36.95		 191504	54.57		 191505	58.17		 191506	66.07		 191507	71.01		 191508	70.16		 191509	64.42		 191510	55.35		 191511	43.11		 191512	33.17		 191601	28.22		 191602	33.03		 191603	42.15		 191604	50.25		 191605	59.31		 191606	66.31		 191607	74.28		 191608	71.82		 191609	63.5		 191610	52.14		 191611	40.23		 191612	28.94		 191701	28.27		 191702	30.09		 191703	38.35		 191704	48.63		 191705	55.13		 191706	66.97		 191707	74.61		 191708	71.02		 191709	64.09		 191710	50.41		 191711	43.54		 191712	29.64		 191801	23.86		 191802	33.82		 191803	45.75		 191804	49.03		 191805	60.8		 191806	71.15		 191807	72.45		 191808	72.5		 191809	61.92		 191810	56.17		 191811	40.51		 191812	34.45		 191901	31.82		 191902	32.25		 191903	40.89		 191904	51.35		 191905	60.03		 191906	69.3		 191907	74.35		 191908	72.27		 191909	65.64		 191910	52.59		 191911	39.31		 191912	28.78		 192001	29.23		 192002	33.69		 192003	40.28		 192004	46.78		 192005	59.31		 192006	67.37		 192007	72.7		 192008	70.63		 192009	65.44		 192010	54.63		 192011	39.7		 192012	33.13		 192101	34.36		 192102	36.9		 192103	46.63		 192104	51.01		 192105	60.1		 192106	70.36		 192107	74.66		 192108	72.03		 192109	66.54		 192110	55.35		 192111	42.58		 192112	35.08		 192201	26.8		 192202	31.95		 192203	40.42		 192204	50.31		 192205	61.18		 192206	70.14		 192207	73		 192208	72.81		 192209	67.28		 192210	55.02		 192211	41.86		 192212	33.55		 192301	34.59		 192302	29.57		 192303	38.3		 192304	49.91		 192305	59.52		 192306	68.04		 192307	73.76		 192308	71.11		 192309	65.07		 192310	51.24		 192311	42.58		 192312	35.98		 192401	26.26		 192402	35.19		 192403	37.18		 192404	50.27		 192405	57.9		 192406	68.59		 192407	71.89		 192408	72.07		 192409	62.74		 192410	54.97		 192411	42.4		 192412	27.59		 192501	29.08		 192502	38.3		 192503	44.24		 192504	54.72		 192505	60.01		 192506	69.84		 192507	74.14		 192508	71.4		 192509	66.67		 192510	48.92		 192511	40.41		 192512	32.5		 192601	30.31		 192602	37.67		 192603	39.65		 192604	50.04		 192605	61.02		 192606	68.2		 192607	73.36		 192608	72.34		 192609	64.11		 192610	54.95		 192611	40.46		 192612	31.33		 192701	31.55		 192702	37.9		 192703	42.26		 192704	51.58		 192705	59.76		 192706	67.21		 192707	72.68		 192708	69.37		 192709	64.98		 192710	55.9		 192711	44.35		 192712	28.22		 192801	31.98		 192802	34.34		 192803	43.12		 192804	48.06		 192805	61.52		 192806	65.91		 192807	73.4		 192808	71.82		 192809	63.27		 192810	55.08		 192811	41.58		 192812	32.94		 192901	26.31		 192902	26.92		 192903	43.56		 192904	51.17		 192905	58.86		 192906	67.5		 192907	73.6		 192908	72.63		 192909	63.41		 192910	53.92		 192911	38.41		 192912	33.96		 193001	23.54		 193002	40.1		 193003	40.41		 193004	54.41		 193005	59.23		 193006	68.41		 193007	75.04		 193008	72.9		 193009	65.75		 193010	51.69		 193011	41.09		 193012	31.17		 193101	32.99		 193102	37.94		 193103	39.42		 193104	51.06		 193105	59.43		 193106	70.7		 193107	75.81		 193108	71.96		 193109	68.13		 193110	56.57		 193111	43.38		 193112	35.06		 193201	31.55		 193202	36.7		 193203	37.36		 193204	51.6		 193205	60.51		 193206	69.24		 193207	74.1		 193208	72.57		 193209	64.69		 193210	52.32		 193211	40.75		 193212	29.41		 193301	34.3		 193302	29.59		 193303	41.83		 193304	49.84		 193305	59.83		 193306	71.56		 193307	75.13		 193308	71.92		 193309	67.73		 193310	55.2		 193311	42.53		 193312	36.43		 193401	35.08		 193402	34.32		 193403	42.78		 193404	53.74		 193405	64.71		 193406	70.68		 193407	76.37		 193408	73.53		 193409	63.84		 193410	56.52		 193411	45.01		 193412	32.67		 193501	31.51		 193502	36.01		 193503	43.61		 193504	49.71		 193505	57.33		 193506	67.64		 193507	75.13		 193508	72.99		 193509	64.8		 193510	53.8		 193511	39.49		 193512	30.74		 193601	27.36		 193602	25.23		 193603	43.43		 193604	50.22		 193605	63.46		 193606	70.61		 193607	76.8		 193608	74.59		 193609	66.36		 193610	53.49		 193611	39.81		 193612	34.47		 193701	24.84		 193702	31.73		 193703	38.84		 193704	50.11		 193705	61.93		 193706	68.79		 193707	74.59		 193708	74.66		 193709	65.7		 193710	53.89		 193711	40.82		 193712	32.7		 193801	32.14		 193802	36		 193803	45.01		 193804	51.73		 193805	59.85		 193806	68.77		 193807	73.78		 193808	73.72		 193809	66.63		 193810	56.41		 193811	39.94		 193812	34.21		 193901	33.91		 193902	29.98		 193903	42.51		 193904	51.53		 193905	62.71		 193906	68.86		 193907	74.88		 193908	72.64		 193909	67.37		 193910	54.72		 193911	42.3		 193912	37.72		 194001	23.83		 194002	33.85		 194003	41.52		 194004	50.23		 194005	60.85		 194006	69.6		 194007	74.14		 194008	72.14		 194009	65.35		 194010	56.08		 194011	39		 194012	36.05		 194101	32.2		 194102	33.53		 194103	39.2		 194104	52.02		 194105	62.33		 194106	67.8		 194107	73.98		 194108	72.07		 194109	64.53		 194110	55.2		 194111	42.91		 194112	36.12		 194201	29.84		 194202	30.74		 194203	41.31		 194204	53.06		 194205	59.09		 194206	67.91		 194207	73.96		 194208	71.78		 194209	63.66		 194210	54.57		 194211	43.16		 194212	32.97		 194301	29.41		 194302	36.28		 194303	38.5		 194304	52.88		 194305	59.72		 194306	68.77		 194307	74.26		 194308	73.45		 194309	64.33		 194310	53.69		 194311	40.91		 194312	32.59		 194401	32.02		 194402	34.5		 194403	38.5		 194404	48.97		 194405	62.02		 194406	68.36		 194407	72.79		 194408	72.1		 194409	65.26		 194410	55.27		 194411	41.5		 194412	30.67		 194501	30.49		 194502	35.28		 194503	45.54		 194504	50.22		 194505	58.28		 194506	65.88		 194507	72.93		 194508	72.16		 194509	64.99		 194510	54.14		 194511	42.01		 194512	29.08		 194601	31.39		 194602	34.88		 194603	46.78		 194604	54.61		 194605	58.75		 194606	68.32		 194607	73.85		 194608	71.17		 194609	64.54		 194610	53.15		 194611	41.74		 194612	36.18		 194701	31.78		 194702	31.41		 194703	38.75		 194704	50.95		 194705	60.13		 194706	66.72		 194707	72.81		 194708	74.08		 194709	66.54		 194710	58.8		 194711	38.1		 194712	32.92		 194801	27.88		 194802	31.62		 194803	38.71		 194804	53.35		 194805	60.24		 194806	68.76		 194807	73.26		 194808	72.05		 194809	66.07		 194810	53.19		 194811	41.59		 194812	32.58		 194901	25.92		 194902	31.91		 194903	40.77		 194904	52.07		 194905	61.72		 194906	69.24		 194907	74.21		 194908	72.1		 194909	63.73		 194910	54.05		 194911	45.27		 194912	33.26		 195001	30.43		 195002	35.55		 195003	38.84		 195004	48.65		 195005	59.45		 195006	67.93		 195007	71.22		 195008	70.02		 195009	63.5		 195010	57.47		 195011	40.64		 195012	33.01		 195101	30.2		 195102	34.54		 195103	38.55		 195104	49.73		 195105	60.76		 195106	66.65		 195107	73.69		 195108	71.89		 195109	64.09		 195110	54		 195111	38.08		 195112	31.23		 195201	32		 195202	35.46		 195203	37.69		 195204	51.66		 195205	60.58		 195206	70.75		 195207	74.1		 195208	72.82		 195209	65.89		 195210	52.95		 195211	39.92		 195212	33.44		 195301	36.43		 195302	35.87		 195303	43.75		 195304	48.76		 195305	59.18		 195306	70.18		 195307	74.17		 195308	72.1		 195309	66.16		 195310	56.21		 195311	43.88		 195312	33.69		 195401	30.9		 195402	41.41		 195403	39.25		 195404	54.18		 195405	58.59		 195406	68.85		 195407	75.47		 195408	72.18		 195409	66.45		 195410	54.68		 195411	44.06		 195412	33.91		 195501	29.35		 195502	31.05		 195503	40.06		 195504	52.86		 195505	61.29		 195506	66.54		 195507	74.44		 195508	73.87		 195509	65.88		 195510	55.04		 195511	38.23		 195512	31.71		 195601	31.01		 195602	32.27		 195603	40.75		 195604	49.37		 195605	61.77		 195606	70.36		 195607	73.06		 195608	71.69		 195609	65.1		 195610	56.16		 195611	40.32		 195612	36.23		 195701	27.07		 195702	38.07		 195703	41.27		 195704	50.7		 195705	59.65		 195706	68.7		 195707	74.28		 195708	71.65		 195709	64.18		 195710	51.67		 195711	40.26		 195712	37		 195801	31.6		 195802	31.98		 195803	37.67		 195804	50.27		 195805	62.42		 195806	67.93		 195807	72.63		 195808	73.29		 195809	65.43		 195810	54.73		 195811	43.02		 195812	32.22		 195901	29.5		 195902	32.49		 195903	41.45		 195904	51.6		 195905	60.84		 195906	69.96		 195907	73.58		 195908	73.17		 195909	64.74		 195910	53.33		 195911	38.66		 195912	35.94		 196001	29.46		 196002	30.52		 196003	35.91		 196004	52.59		 196005	59.31		 196006	69.08		 196007	73.89		 196008	72.21		 196009	66.45		 196010	54.77		 196011	42.73		 196012	30.4		 196101	29.71		 196102	37.42		 196103	43.47		 196104	48.67		 196105	58.87		 196106	69.49		 196107	73.24		 196108	72.7		 196109	63.41		 196110	53.85		 196111	40.5		 196112	31.08		 196201	26.96		 196202	34.92		 196203	37.9		 196204	51.84		 196205	62.24		 196206	67.91		 196207	72.07		 196208	72.12		 196209	64.18		 196210	56.12		 196211	43.18		 196212	33.4		 196301	24.44		 196302	34.12		 196303	43.72		 196304	51.89		 196305	61.02		 196306	68.67		 196307	73.6		 196308	71.98		 196309	66.34		 196310	59.36		 196311	44.04		 196312	27.9		 196401	31.53		 196402	31.77		 196403	38.82		 196404	51.3		 196405	61.43		 196406	68		 196407	74.66		 196408	70.72		 196409	63.7		 196410	53.78		 196411	42.33		 196412	32.04		 196501	31.8		 196502	32.52		 196503	35.44		 196504	51.89		 196505	60.8		 196506	66.85		 196507	72.61		 196508	71.06		 196509	61.77		 196510	54.99		 196511	44.65		 196512	35.85		 196601	26.38		 196602	31.24		 196603	43		 196604	49.96		 196605	60.19		 196606	67.93		 196607	75.07		 196608	70.86		 196609	64.54		 196610	52.83		 196611	43.21		 196612	32.68		 196701	33.1		 196702	32.88		 196703	43.63		 196704	51.01		 196705	57.63		 196706	67.55		 196707	72.52		 196708	71.22		 196709	64.06		 196710	53.92		 196711	41.54		 196712	32.07		 196801	28.94		 196802	32.92		 196803	43.56		 196804	50.58		 196805	58.17		 196806	68.5		 196807	72.86		 196808	70.59		 196809	63.9		 196810	54.64		 196811	41.14		 196812	30.04		 196901	29.37		 196902	32.81		 196903	36.03		 196904	52.63		 196905	61.41		 196906	66.83		 196907	74.1		 196908	73.22		 196909	65.55		 196910	51.03		 196911	41.59		 196912	33.46		 197001	27.14		 197002	35.35		 197003	38.5		 197004	49.44		 197005	61.07		 197006	68.74		 197007	73.96		 197008	73.38		 197009	64.58		 197010	52.27		 197011	41.31		 197012	33.58		 197101	29.41		 197102	33.48		 197103	39.65		 197104	50.27		 197105	58.26		 197106	69.44		 197107	72.36		 197108	72.01		 197109	64.33		 197110	55.08		 197111	41.61		 197112	33.98		 197201	29.93		 197202	33.55		 197203	44.04		 197204	50.81		 197205	60.53		 197206	68.22		 197207	72.18		 197208	71.67		 197209	64.44		 197210	52.29		 197211	38.93		 197212	29.86		 197301	29.59		 197302	33.58		 197303	44.29		 197304	48.83		 197305	59.23		 197306	68.95		 197307	73.26		 197308	72.61		 197309	64.4		 197310	56.07		 197311	42.93		 197312	33.71		 197401	31.01		 197402	34.74		 197403	44.38		 197404	51.55		 197405	60.37		 197406	68.49		 197407	74.08		 197408	70.3		 197409	62.31		 197410	53.89		 197411	42.39		 197412	33.66		 197501	32.34		 197502	32.76		 197503	38.7		 197504	46.85		 197505	60.35		 197506	67.51		 197507	73.56		 197508	71.53		 197509	62.89		 197510	54.63		 197511	42.6		 197512	34.29		 197601	29.93		 197602	39.56		 197603	42.31		 197604	51.85		 197605	59.04		 197606	67.8		 197607	72.9		 197608	70.66		 197609	64.18		 197610	50		 197611	38.48		 197612	30.92		 197701	23.09		 197702	36.03		 197703	43.18		 197704	54.07		 197705	61.66		 197706	70.34		 197707	74.43		 197708	71.78		 197709	65.93		 197710	53.98		 197711	42.87		 197712	33.28		 197801	25.86		 197802	27.99		 197803	41.31		 197804	51.58		 197805	59.74		 197806	68.94		 197807	73.8		 197808	71.8		 197809	65.84		 197810	54.41		 197811	41.47		 197812	29.8		 197901	21.9		 197902	28.13		 197903	42.06		 197904	50.14		 197905	59.13		 197906	67.82		 197907	73.13		 197908	70.97		 197909	66.09		 197910	55.26		 197911	39.94		 197912	36.03		 198001	31.12		 198002	32.85		 198003	39.36		 198004	51.44		 198005	60.28		 198006	68.74		 198007	75.76		 198008	72.79		 198009	66.24		 198010	52.59		 198011	42.31		 198012	35.19		 198101	32.41		 198102	36.59		 198103	42.85		 198104	55.13		 198105	58.96		 198106	69.82		 198107	73.96		 198108	72.1		 198109	64.92		 198110	52.32		 198111	44.74		 198112	33.66		 198201	26.22		 198202	32.59		 198203	42

Dominic · Accepted Answer

2
ASSESSMENT TASK 2
Contents
Question 1: Summary	3
Question 2: Visualise	3
Question 3: Geometric Brownian Motion	4
Question 4:	4
Question 5:	7
Question 6:	8
Appendix	8
References	9
Question 1: Summary
The following table gives initial summary of the data
	Student ID 
	 
	Period
	Jan 1959 - Jan 1979
	Min
	23.09
	Median
	52.28
	Mean
	51.74
	Max
	75.07
Question 2: Visualise
R command for plotting data using ggplot package produces the following plot. The series seems to follow oscillate up and down about the mean across the time period. 
Figure 1: Time series plot of the data
       
Visually, the plot doesn’t seem to give off any evidence towards upward or downward trends. The mean of the data is calculated to be 51.74 and the variance to be around 238.836. 
The histogram also doesn’t seem to suggest any thing particular about the series.
Figure 2: Histogram of Value
Question 3: Geometric Brownian Motion
A stochastic process is a process that is random in time. That is, value Xi in each time period ti a random variable. 
A geometric Brownian motion is a type of Stochastic process in which evolves in such a way that relative change of the series is a Brownian motion.
Solving for S and simplifying, we get;
μ and σ, are the instantaneous mean and instantaneous standard deviation of the process, that is mean per unit of time and standard deviation per unit of time
Question 4:
In order for a stochastic process to satisfy the condition of being a Geometric Brownian motion;
· E( = ,    
· Since relative change in S is normally distributed, S will be log-normally distributed with parameters μ and σ,

Contiguous U.S. Average Temperature Units: Degrees Fahrenheit Base Period: XXXXXXXXXX Missing: -99 DateValue 18990129.68 18990225.5 18990337.63 18990450.61 18990559.9 18990668.65 18990773.08...

Answer To: Contiguous U.S. Average Temperature Units: Degrees Fahrenheit Base Period: XXXXXXXXXX Missing: -99...

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