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Explain and justify your answer. + +The MSE is defined almost the same as variance, given by +$$ +\frac{\sum{(x-\overline{x})^2}}{n} +$$ +# Activity 3 +Prove that the following holds for Gamma distribution: +$$ +\alpha = \frac{\overline{x}^2}{s^2} +$$ +$$ +\beta = \frac{s^2}{\overline{x}} +$$ + +Which results by substition from the following: +$$ \overline{x} = \alpha \beta, \quad s^2 = \alpha \beta^2 $$ +$$ +\alpha \left(\frac{\overline{x}}{\alpha}\right)^2 = s ^2 +$$ +yielding the first definition for $\alpha$. +Substituting into the expression for $\beta$ results in +$$ +\beta = \frac{\overline{x}}{\alpha} = \frac{\overline{x}}{\frac{\overline{x}^2}{s^2}} = \frac{s^2}{\overline{x}} +$$ diff --git a/record.25o b/record.25o new file mode 100644 index 0000000..8ad3fe5 --- /dev/null +++ b/record.25o @@ -0,0 +1,12260 @@ + 3.04 OBSERVATION DATA M: Mixed RINEX VERSION / TYPE +Geo++ RINEX Logger Geo++ 20251022 171240 UTC PGM / RUN BY / DATE +************************************************************COMMENT +This file was generated by the Geo++ RINEX Logger App COMMENT +for Android devices (Version 2.1.8). If you encounter COMMENT +any issues, please send an email to android@geopp.de COMMENT +Filtering Mode: BEST COMMENT +************************************************************COMMENT +Hardware: MediaTek,MT,MTK_MNLD_14_1.00,MNL_VER_24100901ALPS05_8.00_00COMMENT +Geo++ MARKER NAME +GEODETIC MARKER TYPE +Geo++ Geo++ OBSERVER / AGENCY +NA NA NA REC # / TYPE / VERS +NA NA ANT # / TYPE + 4315068.1124 1200384.6863 4525913.8754 APPROX POSITION XYZ + 0.0000 0.0000 0.0000 ANTENNA: DELTA H/E/N +G 8 C1C L1C D1C S1C C5Q L5Q D5Q S5Q SYS / # / OBS TYPES +R 4 C1C L1C D1C S1C SYS / # / OBS TYPES +E 12 C1B L1B D1B S1B C1C L1C D1C S1C C5Q L5Q D5Q S5Q SYS / # / OBS TYPES +C 12 C2I L2I D2I S2I C1D L1D D1D S1D C5P L5P D5P S5P SYS / # / OBS TYPES +J 8 C1C L1C D1C S1C C5Q L5Q D5Q S5Q SYS / # / OBS TYPES + 2025 10 22 17 12 58.0009999 GPS TIME OF FIRST OBS + 24 R01 1 R02 -4 R03 5 R04 6 R05 1 R06 -4 R07 5 R08 6 GLONASS SLOT / FRQ # + R09 -2 R10 -7 R11 0 R12 -1 R13 -2 R14 -7 R15 0 R16 -1 GLONASS SLOT / FRQ # + 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17:17:21.000 45.492328354 15.549180485 162.1560 5 7 100.5915 72.6957 229.3849 -25.0855 66.6331 -74.8327 0.00 0.0 +2025/10/22 17:17:22.000 45.492333231 15.549188777 161.1905 5 7 100.5884 72.6985 229.4013 -25.1001 66.6404 -74.8243 0.00 0.0 +2025/10/22 17:17:23.000 45.492330535 15.549196406 160.1465 5 7 100.5854 72.7014 229.4176 -25.1147 66.6476 -74.8158 0.00 0.0 +2025/10/22 17:17:24.000 45.492324559 15.549214463 159.7576 5 7 100.5823 72.7042 229.4340 -25.1292 66.6548 -74.8072 0.00 0.0 +2025/10/22 17:17:25.000 45.492335643 15.549206320 160.1744 5 7 100.5792 72.7071 229.4502 -25.1439 66.6622 -74.7988 0.00 0.0 +2025/10/22 17:17:26.000 45.492336879 15.549223799 159.6161 5 7 100.5761 72.7100 229.4665 -25.1584 66.6694 -74.7903 0.00 0.0 +2025/10/22 17:17:27.000 45.492330346 15.549229951 158.8229 5 7 100.5730 72.7128 229.4828 -25.1730 66.6766 -74.7818 0.00 0.0 +2025/10/22 17:17:28.000 45.492325333 15.549249522 158.4957 5 7 100.5699 72.7157 229.4990 -25.1875 66.6838 -74.7732 0.00 0.0 +2025/10/22 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17:17:37.000 45.492361372 15.549386855 157.4647 5 7 100.5423 72.7414 229.6440 -25.3180 66.7480 -74.6966 0.00 0.0 +2025/10/22 17:17:38.000 45.492361167 15.549402528 159.3497 5 7 100.5392 72.7442 229.6600 -25.3325 66.7551 -74.6881 0.00 0.0 +2025/10/22 17:17:39.000 45.492371283 15.549418175 158.7084 5 7 100.5361 72.7471 229.6760 -25.3469 66.7622 -74.6796 0.00 0.0 +2025/10/22 17:17:40.000 45.492370570 15.549444500 159.0860 5 7 100.5330 72.7500 229.6919 -25.3613 66.7692 -74.6710 0.00 0.0 +2025/10/22 17:17:41.000 45.492368321 15.549475116 158.4299 5 7 100.5300 72.7528 229.7079 -25.3757 66.7762 -74.6624 0.00 0.0 +2025/10/22 17:17:42.000 45.492363165 15.549509535 157.7436 5 7 100.5269 72.7556 229.7238 -25.3901 66.7832 -74.6538 0.00 0.0 +2025/10/22 17:17:43.000 45.492197809 15.549668761 203.5885 5 8 86.6205 65.1314 178.2216 31.7621 -15.5110 42.6978 0.00 0.0 +2025/10/22 17:17:44.000 45.492119283 15.549757199 226.7056 5 8 86.6188 65.1317 178.2457 31.7535 -15.5033 42.7047 0.00 0.0 +2025/10/22 17:17:45.000 45.492146983 15.549737672 215.2649 5 8 86.6172 65.1320 178.2701 31.7449 -15.4944 42.7111 0.00 0.0 +2025/10/22 17:17:46.000 45.492134107 15.549754622 211.7411 5 8 86.6157 65.1324 178.2944 31.7362 -15.4859 42.7177 0.00 0.0 +2025/10/22 17:17:47.000 45.492133029 15.549778229 210.0120 5 8 86.6141 65.1327 178.3187 31.7276 -15.4774 42.7242 0.00 0.0 +2025/10/22 17:17:48.000 45.492141281 15.549768765 201.4085 5 8 86.6125 65.1331 178.3430 31.7189 -15.4686 42.7307 0.00 0.0 +2025/10/22 17:17:49.000 45.492144700 15.549768358 199.8672 5 8 86.6109 65.1334 178.3673 31.7103 -15.4598 42.7372 0.00 0.0 +2025/10/22 17:17:50.000 45.492134500 15.549785122 199.5106 5 8 86.6093 65.1338 178.3916 31.7017 -15.4513 42.7437 0.00 0.0 +2025/10/22 17:17:51.000 45.492138518 15.549794217 200.4010 5 8 86.6077 65.1341 178.4158 31.6930 -15.4426 42.7502 0.00 0.0 +2025/10/22 17:17:52.000 45.492112365 15.549828818 204.6912 5 8 86.6061 65.1344 178.4400 31.6844 -15.4342 42.7567 0.00 0.0 +2025/10/22 17:17:53.000 45.492127527 15.549806208 195.2232 5 8 86.6045 65.1348 178.4643 31.6757 -15.4251 42.7631 0.00 0.0 +2025/10/22 17:17:54.000 45.492124693 15.549806305 193.3131 5 8 86.6029 65.1351 178.4886 31.6670 -15.4163 42.7696 0.00 0.0 +2025/10/22 17:17:55.000 45.492122743 15.549808256 191.4466 5 8 86.6013 65.1355 178.5128 31.6584 -15.4075 42.7760 0.00 0.0 +2025/10/22 17:17:56.000 45.492128762 15.549818962 189.6170 5 8 86.5997 65.1358 178.5371 31.6497 -15.3988 42.7824 0.00 0.0 +2025/10/22 17:17:57.000 45.492127602 15.549828407 187.7861 5 8 86.5981 65.1362 178.5613 31.6410 -15.3901 42.7889 0.00 0.0 +2025/10/22 17:17:58.000 45.492121359 15.549823753 185.1801 5 8 86.5965 65.1365 178.5855 31.6324 -15.3812 42.7953 0.00 0.0 +2025/10/22 17:17:59.000 45.492124295 15.549834220 182.4605 5 8 86.5949 65.1369 178.6097 31.6237 -15.3724 42.8017 0.00 0.0 +2025/10/22 17:18:00.000 45.492121932 15.549838752 182.2536 5 8 86.5933 65.1372 178.6339 31.6150 -15.3636 42.8081 0.00 0.0 +2025/10/22 17:18:01.000 45.492115578 15.549849029 183.9497 5 8 86.5917 65.1376 178.6581 31.6063 -15.3548 42.8145 0.00 0.0 +2025/10/22 17:18:02.000 45.492109729 15.549855223 182.7983 5 8 86.5901 65.1379 178.6823 31.5977 -15.3460 42.8208 0.00 0.0 +2025/10/22 17:18:03.000 45.492103307 15.549856899 181.7073 5 8 86.5885 65.1383 178.7065 31.5890 -15.3371 42.8272 0.00 0.0 +2025/10/22 17:18:04.000 45.492092646 15.549858364 182.6047 5 8 86.5869 65.1386 178.7306 31.5803 -15.3282 42.8336 0.00 0.0 +2025/10/22 17:18:05.000 45.492085953 15.549852663 181.7283 5 8 86.5853 65.1390 178.7548 31.5716 -15.3192 42.8400 0.00 0.0 +2025/10/22 17:18:06.000 45.492076109 15.549852097 182.9370 5 8 86.5837 65.1393 178.7789 31.5629 -15.3102 42.8464 0.00 0.0 +2025/10/22 17:18:07.000 45.492075008 15.549857074 182.8431 5 8 86.5821 65.1397 178.8030 31.5542 -15.3013 42.8527 0.00 0.0 +2025/10/22 17:18:08.000 45.492072163 15.549832453 177.2529 5 7 100.4468 72.8301 230.1292 -25.7618 66.9642 -74.4272 0.00 0.0 +2025/10/22 17:18:09.000 45.492060392 15.549819034 177.4534 5 7 100.4438 72.8330 230.1445 -25.7761 66.9712 -74.4184 0.00 0.0 +2025/10/22 17:18:10.000 45.492055536 15.549825088 180.0967 5 7 100.4407 72.8358 230.1597 -25.7903 66.9781 -74.4096 0.00 0.0 +2025/10/22 17:18:11.000 45.492037654 15.549817300 182.6539 5 7 100.4376 72.8387 230.1749 -25.8045 66.9850 -74.4008 0.00 0.0 +2025/10/22 17:18:12.000 45.491921872 15.549757262 166.6496 5 7 100.4344 72.8417 230.1904 -25.8187 66.9923 -74.3914 0.00 0.0 +2025/10/22 17:18:13.000 45.491739075 15.549785358 184.4391 5 8 86.5726 65.1418 178.9478 31.5018 -15.2467 42.8922 0.00 0.0 +2025/10/22 17:18:14.000 45.491840662 15.549714623 154.7513 5 7 100.4283 72.8475 230.2209 -25.8471 67.0063 -74.3734 0.00 0.0 +2025/10/22 17:18:15.000 45.491826865 15.549714822 156.4410 5 7 100.4252 72.8504 230.2360 -25.8612 67.0132 -74.3646 0.00 0.0 +2025/10/22 17:18:16.000 45.491695089 15.549836414 197.3808 5 8 86.5678 65.1428 179.0199 31.4757 -15.2201 42.9111 0.00 0.0 diff --git a/record_events.pos b/record_events.pos new file mode 100644 index 0000000..45494c5 --- /dev/null +++ b/record_events.pos @@ -0,0 +1 @@ +% GPST latitude(deg) longitude(deg) height(m) Q ns sdn(m) sde(m) sdu(m) sdne(m) sdeu(m) sdun(m) age(s) ratio