Save trees use e-Question Paper Go green DOWNLOAD THIS FREE AT www.viuresource.com GCS Sculls isn l Ismay Fourth Semester B.E. Degree Examination, June/July 2023 O Complex Analysis, Probability and Statistical Met ime: 3 hrs. Max. Mie: 1g Note: Answer any FIVE full questions, choosing ONE full question from each modu Modute=1 Find analytic funetion u + iv, where wis given to be w= I(x? ~ 4) ely fry 106 Marks (07 Marks) Derive Cauchy Reimann equations in polar form, Show that u=e™ [xeos2y-~ ysin2y] 1s harmonic. Find the anaflie nie) ~u (07 Marks) Modute2 Find the Bilinear tansformation [s2= 1, -Lomow = 0,1, vatuats _f(2)* along pn w2ty on 8 Discuss the transforma P (06 stares) State and prove Cau = i 07 Maries © Evaluate using C al formal i c (7 Marky Moaule-3 a ma Fariable ii) Discrete probability distribution with an example i ® ty that man aged 60 will Live upto 70 is 0.65. What i the probability that 0 7 10 metimpized' 60" i) Exactly 9 i) atmost9 i) Atleast 7 will live up 0 age ot i ‘nggmal distribution, 396 of tems are under 45 ane! 89% are over 64, Find the mess s (AF deviation, given that A(0S) = 019 and A(LA)= 0.82 (oF Mansy 1 of3 BRANCHES | ALL SEMESTERS | NOTES | QUESTON PAPERS | LAB MANUALS A Vturesource Go Green initiativeSave trees use e-Question Paper DOWNLOAD THIS FREE AT www.viuresource.com ISMATAE or te random variable X is given by 2[-aifo 11213 Tae [os 1K] The probability distribution ofa x (poo torte tos ta nul °K", mean and varianee of X be Iprobabilty oF bad reaction fom certain injection is 0.001. Determine the charg 0f°3000 individuals more than two will et tad reaction, and ess than {wo ©The frequeney of accidents per shit $8 shown in se following table Ace aoa Frequency | 192| 100 | 24 3} 1) Calculate mean numbers oF aseidents per Sil. Find the eo spondiny (7 Nass) 8 Fita seconel degree parabola y = a + bx cx" for the Follow ingflta xjolif2[3[43] yiilsi7[3 lar]; (06 Marks) Find the coefficient of correlation lines of regression of Wy and ¥ on x. Given, pu (7 Mark) f: (er any (oo sti) Find the rank correlation he following da: i 08] 71/816 | 10] 32) 31 ag fon) es [733 [s1] 22] (o7stactn és sits, 7 oid ein woo Maing i tenuis stay 32.5, (07 Mart Modules bution for follow ng data a[4 1_jorjoz) 0 [03] (2 to2tororto Doterminette marginal distributions of X and ¥ also calculate B(x), B(9), COV (xy) {as Marks) limits i) Type, Type Terrors, (07 Marks} pQpetingi Nou nypornesis ip Contide 2of3 A Vturesource Go Green initiative Go green BRANCHES | ALL SEMESTERS | NOTES | QUESTON PAPERS | LAB MANUALSSave trees use e-Question Paper Go green DOWNLOAD THIS FREE AT www.viuresource.com ASMATAL The fllowing table gives the distribution of digit inthe numbers chosen at random fo telephone die states : Y on ee eee EEA oa pee av montersTboat, ~~ Frias darbuton af ond 2) Soin proeniy durian of and Y Deere andr sete Pivaet ts cree diam et tbepeicen eee fc mne tetecmtt disoa orpapasin phate nani 1k ah ange ern 280k Tee Soiteence lal at 03 vel Se eae cy a opebe tian Me ae re yas fc ge Magueonet ies tuners is 66" (ialuc of te = 2.262 for 9. Sy oe or S S RY « 30f3 BRANCHES | ALL SEMESTERS | NOTES | QUESTON PAPERS | LAB MANUALS A Vturesource Go Green initiative