Question

QUESTIONS 1) [5Opts) Two random variables X and Y have have the following joint distribution. A rondom variable Z is known to be the sum of these two random variables. The joint probability distribution of X and Y is given as fxy(x,y) = kye-*e-> 0<x0<y Calculate var(2) 2) [50pts] Given the joint distribution function OS Xys 1 Calculate A and B 0.07 0.00 0.00 0.5000 0.5398 0.5793 0.6179 0.6554 0.6915 0.7257 0.7580 0.7881 0.8150 0.8413 0.8643 Z 0.0 0.1 0.2 03 04 05 0.6 0.7 0.8 0.9 1.0 1.1 1.2 13 1.4 15 1.6 1.7 1.8 1.9 2.0 2.1 22 23 24 25 2.6 2.7 28 2.9 0.01 0.5040 0.5438 0.5832 0.6217 0.6591 0.6950 0.7291 0.7511 0.7910 0.8186 0.8438 0.8665 0.8869 0.9049 0.9207 0.9345 0.9463 0.9564 0.9649 0.9719 0.9778 0.9826 0.9864 0.9896 0.9920 0.9940 0.9955 0.9966 0.9975 0.9982 0.02 0.5080 0.5470 0.5871 0.6255 0.6628 0.6985 0.7324 0.7642 0.7939 0.8212 0.8461 0.8686 0.8930 0.9066 0.9222 0.9357 0.9474 0.9573 0.9656 0.9726 0.9783 0.9830 0.9860 0.9890 0.9922 0.9941 0.9032 0.9192 0.9332 0.9452 0.9554 0.9641 0.9713 0.9772 0.9821 0.9861 0.9893 0.9918 0.9938 0.9953 0.9965 0.9974 0.9981 0.03 0.5120 0.5517 0.5910 0.6293 0.6664 0.7019 0.7357 0.7673 0.7967 0.8238 0.8485 0.8708 0.8907 0.9082 0.9236 0.9370 0.9484 0.9582 0.9664 0.9732 0.9788 0.9834 0.987: 0.990: 0.9924 0.9943 0.9957 0.9968 0.9977 0.9983 0.04 0.5160 0.5557 0.5948 0.6331 0.6700 0.7054 0.7389 0.7704 0.7995 0.8254 0.8508 0.8729 0.8925 0.9099 0.9251 0.9382 0.9495 0.9591 0.9671 0.9738 0.9793 0.9838 0.9875 0.9904 0.9927 0.9945 0.9958 0.9969 0.9977 0.9984 0.05 0.5199 0.5596 0.5907 0.6368 0.6736 0.7088 0.7422 0.7734 0.8023 0.8289 0.8531 0.8749 0.8944 0.9115 0.9265 0.9394 0.9505 0.9599 0.9678 0.9744 0.9798 0.9842 0.9070 0.9906 0.9929 0.9946 0.9960 0.9970 0.9978 0.9984 0.06 0.5239 0.5636 0.6025 0.6406 0.6772 0.7123 0.7454 0.7754 0.8051 0.8315 0.8554 0.8770 0.8962 0.9031 0.9279 0.9406 0.9515 0.9608 0.9686 0.9750 0.9803 0.9846 0.9881 0.9909 0.9931 0.9940 0.9961 0.9971 0.9979 0.9985 0.5279 0.5675 0.6064 0.640 0.6808 0.7157 0.7486 0.7794 0.8078 0.8340 0.8577 0.8790 0.8980 0.9147 0.9292 0.9418 0.9525 0.9516 0.9693 0.9756 0.9808 0.9850 0.9884 0.9911 0.9932 0.5319 0.5714 0.6103 0.6480 0.6844 0.7190 0.7517 0.7823 0.8106 0.8365 0.8599 0.8810 0.8997 0.9162 0.9306 0.9429 0.9535 0.9625 0.9699 0.9761 0.9812 0.9854 0.9887 0.9913 0.9934 0.9951 0.9963 0.9973 0.9980 0.9986 0.09 0.5359 0.5753 0.5141 0.6517 0.6879 0.7224 0.7549 0.2852 0.8133 0.8389 0.8621 0.8830 0.9015 0.9177 0.9319 0.9441 0.9545 0.9633 0.9706 0.9767 0.9817 0.9857 0.9890 0.9916 0.99% 0.9952 0.9954 0.9974 0.9981 0.9986 0.9967 0.990 0.9982 0.9962 0.9972 0.9979 0.9985

please solve both of questions

Answer 1

txil 12,8) k - ye e ocx, ory SS txig (2, 4) dady = 1 ye d da ya -1 + x = & Toeddy fxie (x,y1 = yes, ex are independent il x and 7 and x-engi y ~ 07 (2,1) Let 2 = x + y N121= vlxl+VITI [:x x andy are indeferees ] ad (21 21+2=3. An 2 А 171.9! oza, y el * 1 2² 22 1 1 S: 7., com os alla aj dnes But alldy 114 = FAy+ 0 1 0 = 1 y yz) dy=1 - A + B = 1 -1 B-A - 1 Here 2 unknown (A&BI and equation. Hence the values of A and B who sclisfies estro is the solation