PLEASE TAKE AS MUCH TIME AS YOU NEED TO SOLVE THIS PROBLEM, ALL I NEED IS A CORRECT ANSWER WITH ALL THE STEPS.
I WILL INCLUDE THE Standard normal distribution table JUST IN CASE YOU NEED IT.
THANK YOU!!
. {1) Let X1, ,1!\" he a random sample from a distribution with mean a and variance 0:. (a) Show that ELY; I)? = (2X1?) 11?. (b) Show that ECE XE) = 11012 + oz) [Hint Use linearity of expectation, along with the relation EU\") = Var') + [E(l')]2.] (e) Show that E (11}? 2) = m12 + or". [Hint Apply the similar relation given in the previous hint] 0.09 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 .53188 .53586 +0 50000 50399 50798 51197 51595 51994 52392 52790 57535 +0.1 53983 54380 54776 55172 55567 55966 56360 56749 .57142 58317 .58706 .59095 .59483 59871 .60257 .60642 .61026 61409 +0.2 57926 .62552 62930 .63307 63683 64058 64431 64803 65173 +0.3 61791 62172 +0.4 65542 .65910 66276 66640 67003 67364 67724 .68082 .68439 .68793 .71904 .72240 +0.5 69146 69497 69847 .70194 .70540 .70884 71226 71566 .73565 .73891 .74215 74537 74857 .75175 .75490 +0.6 72575 72907 73237 +0.7 75804 76115 .76424 .76730 77035 77337 77637 77935 .78230 .78524 .81327 +0.8 78814 .79103 79389 .79673 .79955 80234 80511 80785 .81057 81859 .82121 .82381 .82639 82894 83147 .83398 .83646 .83891 +0.9 81594 .85543 .85769 85993 .86214 +1 .84134 84375 .84614 84849 85083 .85314 .86864 87076 87286 87493 87698 87900 .88100 .88298 +1.1 86433 86650 90147 +1.2 88493 88686 .88877 .89065 89251 89435 89617 89796 89973 +1.3 90320 90490 90658 90824 90988 91149 91308 91466 91621 91774 92220 92364 92507 92647 92785 92922 93056 93189 +1.4 91924 92073 +1.5 93319 93448 93574 93699 93822 93943 94062 94179 94295 .94408 +1.6 94520 94630 94738 94845 .94950 95053 .95154 95254 95352 95449 +1.7 95543 95637 95728 95818 .95907 95994 96080 96164 96246 96327 +1.8 96407 96485 96562 96638 .96712 .96784 96856 96926 96995 97062 +1.9 97128 97193 97257 97320 97381 97441 97500 97558 97615 97670 +2 97725 97778 97831 97882 97932 97982 98030 98077 .98124 98169 98257 98300 98341 98382 98422 98461 98500 .98537 98574 +2.1 98214 98809 .98840 98870 98899 +2.2 98610 .98645 98679 98713 98745 98778 99134 .99158 +2.3 98928 .98956 98983 99010 99036 .99061 99086 99111 99324 99343 .99361 +2.4 99180 99202 .99224 99245 99266 .99286 99305 +2.5 .99379 99396 .99413 99430 .99446 99461 99477 99492 99506 99520 +2.6 99534 99547 99560 99573 .99585 99598 99609 99621 99632 99643 +2.7 99653 99664 99674 99683 .99693 99702 99711 99720 .99728 99736 99760 .99767 99774 99781 99788 99795 99801 99807 +2.8 99744 99752 +2.9 99813 99819 99825 99831 99836 99841 99846 99851 .99856 99861 99896 99900 +3 99865 99869 99874 99878 99882 99886 99889 99893 99929 +3.1 99903 99906 99910 99913 99916 99918 99921 99924 99926 99946 99948 99950 +3.2 99931 99934 99936 99938 99940 99942 99944 99962 .99964 99965 +3.3 99952 99953 99955 99957 .99958 99960 99961 99975 99976 +3.4 99966 .99968 .99969 99970 .99971 99972 99973 99974 +3.5 99977 99978 99978 99979 .99980 99981 99981 99982 .99983 99983 99986 .99986 99987 99987 99988 .99988 99989 +3.6 99984 .99985 .99985 .99990 .99990 .99990 99991 99991 99992 99992 .99992 99992 +3.7 99989 +3.8 99993 .99993 99993 99994 99994 99994 99994 .99995 99995 99995 +3.9 99995 99995 99996 99996 99996 99996 99996 99996 99997 .99997 .99998 +4 99997 99997 99997 99997 .99997 99997 .99998 99998 .99998 Table 1. Standard normal distribution table
