Question: 4. (a) Explain the difference between the following statistical distributions: (0) Gaussian (i) Poisson (iii) Binomial Support your answer with engineering examples and state any

4. (a) Explain the difference between the

4. (a) Explain the difference between the following statistical distributions: (0) Gaussian (i) Poisson (iii) Binomial Support your answer with engineering examples and state any relevant equations. [12 marks] (b) A die is rolled a number of times and the results are tabulated below: Score 1 2 2 3 4 5 6 Frequency 17 29 29 20 18 16 Determine if the die is biased using the Chi-Squared test. Show full workings. [13 marks] [25 marks Normal distribution table Table values are for lady for n=0 to 5 where n = x-X 2. o O 0 0.00000 0.1 0.03983 02 0.07926 0.3 0.11791 0.4 0.15542 0.5 0.19148 0.6 0.22575 0.7 0.25803 0.8 0.28814 0.9 0.31594 1 0.34134 1.10.36433 1.2 0.38493 1.3 0.40320 1.40.41924 1.5 0.43319 1.6 0.44520 1.70.45543 1.8 0.46407 1.9 0.47128 2 0.47725 2.1 0.48213 2.2 0.48610 2.3 0.48928 2.4 0.49180 2.5 0.49379 26 0.49534 2.70.49653 2.8 0.49744 2.9 0.49813 3 0.49865 3.5 0.4997673 4 0.4999683 4.5 0.4999966 5 0.4999997133 0.01 0.02 0.03 0.04 0.05 0.08 0.07 0.08 0.09 0.00399 0.00798 0.01197 0.01505 0.01994 0.02392 0.02790 0.03188 0.03586 0.04379 0.04776 0.05172 0.05567 0.05982 0.08356 0.08749 0.07142 0.07534 0.08317 0.08706 0.09095 0,09483 0.09871 0.10257 0.10542 0.11026 0,11409 0.12172 0.12551 0.12930 0.13307 0.13683 0.14058 0.14431 0.14803 0.15173 0.15910 0.16276 0.16640 0.17003 0.17364 0.17724 0.18082 0.18438 0.18793 0.19497 0.19847 0.20194 0.20540 0.20884 021226 0.21566 0.21904 0.22240 0.22907 0.23237 023565 0.23891 0.24215 0.24537 0.24857 0.25175 0.25490 0.261150.20424 0.26730 0.27035 0.27337 0.27637 0.27935 0.28230 0.28523 0.29103 0.29389 0.29873 0.29954 0.30234 0.30510 0.30785 0.31057 0.31327 0.31859 0.32121 0.32381 0.32639 0.32894 0.33147 0.33397 0.33645 0.33891 0.34375 0.34613 0.34849 0.35083 0.35314 0.35543 0.35759 0.35993 0.36214 0.36650 0.36864 0.37076 0.37285 0.37493 0.37697 0.37900 0.38100 0.38297 0.38686 0.38877 0.39065 0.39251 0.39435 0.39616 0.39796 0.39973 0.40147 0.40490 0.40658 0.40824 0.40988 0.41149 0.41308 0.41465 0.41620 0.41773 0.42073 0.42219 0.42364 0.42506 0.42647 0.42785 0.42922 0.43058 0.43189 0.43448 0.43574 0.43699 0.43822 0.43943 0.44062 0.44179 0.44295 0.44408 0.44630 0.44738 0.44845 0.44950 0.45053 0.45154 0.45254 0.45352 0.45448 0.45637 0.45728 0.45818 0.45907 0.45994 0.46079 0.46164 0.46079 0.46184 0.46246 0.46327 0.46485 0.46562 0.46837 0.46711 0.46784 0.46856 0.46926 0.46994 0.47062 0.47193 0.47257 0.47320 0.47381 0.47441 0.47500 0.47558 0.47615 0.47870 0.47778 0.47831 0.47882 0.47932 0.47982 0.48030 0.48077 0.48124 0.48169 0.48257 0.48300 0.48341 0.48382 0.48422 0.48461 0.48500 0.48537 0.48574 0.48545 0.48679 0.48713 0.48745 0.48777 0.48809 0.48840 0.48870 0.48899 0.48956 0.48983 0.49010 0.49038 0.49061 0.49086 0.49111 0.49134 0.49158 0.49202 0.49224 0.49245 0.49266 0.49286 0.49305 0.49324 0.49343 0.49361 0.49396 0.49413 0.49430 0.49446 0.49461 0.49477 0.49491 0.49506 0.49520 0.49547 0.49560 0.49573 0.49585 0.49598 0.49609 0.49621 0.49832 0.49843 0.49664 0.49674 0.49683 0.49693 0.49702 0.49711 0.49720 0.49728 0.49736 0.49752 0.49760 0.49767 0.49774 0.49781 0.49788 0.49795 0.49801 0.49807 0.49819 0.49825 0.49831 0.49838 0.49841 0.49846 0.49851 0.49856 0.49860

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