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Union and Intersection Part 4-Probability-Assignment Solution, Exercises of Probability and Statistics

Homi Bhabha National InstituteProbability and Statistics

Sir Tanika Mukopadhyay taught us Probability at Homi Bhabha National Institute. He gave us assignments so that we can practice what we learned in form of problems. Here is solution to those problems. Its main emphasis is on following points: Equals, Fact, Integrate, Delayed, version, Seconds, previous, Begins, Sketch, Gaussian

Typology: Exercises

2011/2012

Uploaded on 08/03/2012

anandini
anandini 🇮🇳

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Download Union and Intersection Part 4-Probability-Assignment Solution and more Exercises Probability and Statistics in PDF only on Docsity!

Hn #3 Solutions 3.5 a)Sza{z: 0¢2< 25} b) Case 1: Case 2 O2b 3.12 Fylu) = PY < uf 1 Fo(u) utl —— 2 1 i u 1 0 JU PU >d) = 1-PU 36] =1- P[R < 30] = 1 - FalSo] = 9? 3.19 a) We use the fact that the pdf must integrate to one: ©) For x <0, Fx(z) =0; for z > 1, Fx(x) = 1 For 0<2<1 F(a) = f ” Fe(a!da! = 3x? — 20° docsity.com ¢) P Ml [X>t+a|X>i] 2>0 PUX > t+ac}N{X > t}] PIX > tl _ L-Fy(t+2) 1 Fx(e) _ 1 = (1 ~ e7Mtal) “T=(-e*) ee PIX > a] The probability of waiting additional x seconds doesn’t depend on the previous wait- ing time? . It is the same as when one begins to wait. 3.86 X ~ V(0,0%), Power = RX? Foower(y) = P[RX? < y] Pl-yuiRs X'< yh Felu/R) - Be(-/y/R) for, y > 0 felyolPi) 1 fx) 1 fpower(y) = = - afy/R Ro -afyjiR R Exlyfy/R) 4 Ae fel-yy/B) 2yy/R 2yu/R 1 y Vora? Ry ex(— Ja?R) docsity.com 0 y<-a 3.87 a) Fy(z)= 4 Fely) -aSya: Fy) =1 Fy(y) For -a Sy