e8 thx for help ^^
DISTRIBUTION FUNCTION OF THE NORMAL DISTRIBUTION The function tabulated is +() = e- du 0.02 0.03 0.01 0.07 0.09 0.0 0.5000 0.5040 0.5080 0.5120 0.5160 05199 0.5239 0.5279 0.5019 0.5359 0.1 0.5398 0.5438 0.5478 0.5617 0.5557 0.5596 0.5636 0.5675 0.5714 0.5753 0.2 0.5793 0.58.12 0.5571 0.5910 0.5945 0.5947 0.6026 0.6064 0.6103 0.6141 03 0.6179 0.6217 0.6255 0.6293 0.6331 0.6365 0.6-406 0,6443 0.6480 0.6517 04 0.6554 0.6591 0.6628 0.6664 0.6700 0.6736 0.6772 0.680S 0.6844 0.6879 0.5 0.6915 0.6950 0.6985 0.7019 0.7054 0.7048 0.7123 0.7157 0.7190 0.7224 0.6 0.7257 0.7291 0.7324 0.7357 0.7369 0.7422 0.7454 0.7486 0.7517 0.75-49 0.7 0.7580 0.7611 0.76-42 0.7673 0.7704 0.7734 0.7764 0.7794 0.7823 0.7852 0.8 0.7861 0.7910 0.7939 0,7967 0.7995 0.5023 0.8051 0,8078 0.8106 0.8133 0.9 D.8159 0.8186 0.8212 0.8238 0.6264 0.8289 0.8315 0.8340 0.8365 0.8389 1.0 0.8413 0.8438 0.8461 0.8485 0.8508 0.8531 0.8554 0.8577 0.8599 0.8621 1.1. 0.8643 0.8665 0.8686 0.8708 0.6729 0.8749 0.8770 0.8790 0.8810 0.8830 1.2 0.6849 0.6869 0.8858 0.8907 0.8925 0.8944 0.8962 0.8960 0.8997 0.9015 1.3 0.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 0.9177 1.4 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9306 0.9319 1.5 0.9332 0.9345 0.9357 0.9370 0.9382 0.9394 0.9406 0.9418 0.9429 0.94-41 16 0.9452 0.9463 0.9474 0.9484 0.9495 0.9505 0.9515 0.9525 0.9535 0.9545 17 0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 0.9616 0.9625 0.9633 1.H 0.9641 0.9649 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693 0.9649 0.9706 0.9713 0.9719 0.9726 0.9732 0.9735 0.9744 0.9750 0.9756 0.9761 0.9767 2.0 0.97725 0.97778 0.97831 0.97882 0.97932 0.97962 0.98030 0.98077 0.98124 0.98169 2.1 0.98214 0.98257 0.98300 0.98341 0.98382 0.98422 0.98-461 0,98500 0.98537 0.98574 2.2 0.98610 0.98645 0.98679 0.98713 0.98745 0.96778 0.98809 0.98840 0.93870 0.98899 2.3 0.98928 0.98956 0.98983 0.99010 0.99036 0.99061 0.99086 0,99111 0.99134 0.99158 2.4 0.99180 0.99202 0.99224 0.99245 0.99266 0.99286 0.99305 0.99324 0.993-43 0.99361 2.5 0.99379 0.99396 0.90413 0.99430 0.994 46 0.99461 0.99477 0,99492 0.99506 0.99520 2.6 0.99534 0.99547 0.99560 0,99573 0.99585 0.99598 0.99609 0,99621 0.99632 0.99643 17 0.99654 0.99664 0.99674 0,99683 0.99693 0.99702 0.99711 0,99720 0.99728 0.99736 2.8 0.99744 0.99752 0.99760 0.99767 0.99774 199761 0.99788 0.99795 0.99801 0.99807 20 0.99813 0.99819 0.9982 0.99831 0.99836 0.99841 0.99846 0.99851 0.99856 0.99861 3.01 0.99865 0.99869 0.99874 0,99878 0.99682 0.99856 0,99:889 0,99693 0.99896 0.99900 3.1 0.99903 0.90906 0.94910 0,99913 0.99916 0.99918 0.99921 0,99924 0.99926 0.99929 3.1 0.99931 0.99934 0.99936 0.99938 0,999 40 0.999.12 0.99944 0,999 46 0.999-48 0.99950 3.1 0.99952 0.90953 0.99957 0.99958 0.99960 0.99961 0.99962 0.99964 0.99915 3.4 0.99066 0.99969 0.99970 0.99971 0.99972 0.99973 0,99974 0.99975 0.99976 3.5 0.999767 0.999776 0.999784 0.999792 0.999500 0.999817 0.999815 0,999822 0.999828 0.999835 0.999841 0.999847 0.999853 0.999858 0.999564 0.999569 0.999874 0,999879 0.999683 0.999838 1.7 0.999692 0.999896 0.999900 0.999904 0.999908 0.999912 0.999915 0,999918 0.999922 0.999925 0.999925 0.999931 0.999933 0.999936 0.999938 0.999941 0.999943 0,999946 0.999948 0.999950 0,999953 0.999954 0.939956 0.999958 0.999959 0.999961 0.999963 0,999964 0.999966 0.999967There are 10 hunters waiting for ducks to fly by. When a flock of 15 ducks flies overhead, the hunters fire at the same time, but each choose his target at random, independently of the others. Assume that each hunter independently hits his target with probability p. (i) What is the probability that the duck] escapes unhurt for any i=1 .. . .,15? Hint: P(duck j escapes unhurt) = 1:111:21 { duck j escapes unhurt from hunter i}) (ii) Let X be the number of ducks that escape unhurt. Find the expectation of X. (iii) Find the variance of X
