Quiz 7 with Solutions - Mathematics Statistics in Engineer and Science | MATH 483, Quizzes of Mathematical Statistics

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KET Math 483 Quiz #7 Name: Note that the third exam will be on Thursday November 5, 2009. The exam will cover chapters 5,6, and 7, 1- (5 points) Let Y be a random variable having an exponential distribution with @ = 0.75. Use the method of moment-generating functions to find the probability distribution of U=4Y = Mwy (FH = I re | Ci-fé) Gi -0- 4st) Molt\< E Pad = Wy/ 46) iA! = eee See j Ci-eastwe) Cpe) ce), te Bn maf, fo EX 0ansch I Avi bv bu bey WEean Ts ae) VU ‘nos aw EK siasud cue bibuhn wilh meu 2 2- (5 points) Let Y be a random variable having the following probability density function 32 ay TY O 2 SO)= 0 elsewhere Use the method of transformation to find the probability density function of i yest > V2 2ls-w) 9 Me cern) obo) <2. Fytuy = Fy(2s-w): 2 2 (& 4(5-4)*,4 26-4) )o 12(544)h4 4(5-4) wy 4(s-u)(ig-3u), ots 4(S-uj((é-ou) Ys Ucs You Piel: ) Vs Uss Zy KES oO CG YW 3- (5 points) Let Y,,Y,,¥,,Y,,¥; denote a random sample of size 5 from a population with a uniform distribution on the interval (0,8) . Let ¥,) = max(Y,,¥,,¥3,¥,,¥;). Find PY <4) (5) Fiyye L : o YVoe z ool 5k art Sig os dsé Fy. by 25 [ Foi)” Ay) : Nos +7 yy ge a) Frey !4) < » occ) ie 4 a PIN, 14) 2J 2 4y = 2 is hae oO fo 2 \gp